Causal Inference

POLI_SCI 403: Probability and Statistics

Making causal claims

 

How do we know \(X\) causes \(Y\)?

 

Can data help us make causal claims?

 

When is a causal claim not appropriate?

Agenda

• Potential outcomes framework
• Random assignment
• Observational studies
• Quasi-experiments (if we have time)
• Lab

Potential Outcomes Framework

Setup

Notation

• \(D_i = \{0,1\}\) condition (0: control, 1: treatment)

• \(Y_i(D_i)\) is the individual potential outcome

\[ Y_i = \begin{cases} Y_i(0) & : & D_i = 0 \\ Y_i(1) & : & D_i = 1 \end{cases} \]

Switching equation

\[ Y_i = Y_i(1) D_i + Y_i(0) (1 - D_i) \]

Toy example

ID	\(Y_i(1)\)	\(Y_i(0)\)
1	0	0
2	1	0
3	1	0
4	1	1

\(\tau_i = Y_i(1) - Y_i(0)\) is the unit-level treatment effect

 

Toy example

ID	\(Y_i(1)\)	\(Y_i(0)\)	\(\tau_i\)
1	0	0	0
2	1	0	1
3	1	0	1
4	1	1	0

\(\tau_i = Y_i(1) - Y_i(0)\) is the unit-level treatment effect

 

\(E[\tau_i] = \frac{1}{n} \sum_{i=1}^n \tau_i\) is the average treatment effect (ATE)

Assumption

Stable Unit Treatment Value (SUTVA)

Potential outcomes are stable, meaning:

1. No unobserved multiple versions of the treatment: Treatment is the same for everyone

2. No interference: Unit \(i\)’s potential outcome is not affected by \(j\)’s potential outcome

Challenge

ID	\(Y_i(1)\)	\(Y_i(0)\)	\(\tau_i\)
1	0	0	0
2	1	0	1
3	1	0	1
4	1	1	0

Challenge

	Unobserved
ID	\(Y_i(1)\)	\(Y_i(0)\)	\(\tau_i\)
1	0	0	0
2	1	0	1
3	1	0	1
4	1	1	0

Assign condition \(D_i\) (0: control, 1: treatment)

Challenge

	Unobserved			Observed
ID	\(Y_i(1)\)	\(Y_i(0)\)	\(\tau_i\)	\(D_i\)	\(Y_i\)
1	0	0	0	1	0
2	1	0	1	0	0
3	1	0	1	1	1
4	1	1	0	0	1

To know \(E[\tau_i]\) we need \((Y_i(1) - Y_i(0))\)

But we only observe one at a time for each unit

Challenge

	Unobserved			Observed
ID	\(Y_i(1)\)	\(Y_i(0)\)	\(\tau_i\)	\(D_i\)	\(Y_i\)
1	0	0	0	1	0
2	1	0	1	0	0
3	1	0	1	1	1
4	1	1	0	0	1

This is the FUNDAMENTAL PROBLEM OF CAUSAL INFERENCE

The term comes from: Holland, Paul W. 1986. “Statistics and Causal Inference.” Journal of the American Statistical Association 81 (396): 945-960

Challenge

	Unobserved			Observed
ID	\(Y_i(1)\)	\(Y_i(0)\)	\(\tau_i\)	\(D_i\)	\(Y_i\)
1	0	0	0	1	0
2	1	0	1	0	0
3	1	0	1	1	1
4	1	1	0	0	1

How do we approximate \(E[\tau_i]\) with observed data?

ATE decomposition

\[ E[\tau_i] \]

Substitute unit-level treatment effect

ATE decomposition

\[ \begin{align} E[\tau_i] & = E[Y_i(1) - Y_i(0)] \end{align} \]

Apply linearity of expectations

ATE decomposition

\[ \begin{align} E[\tau_i] & = E[Y_i(1) - Y_i(0)] \\ & = E[Y_i(1)] - E[Y_i(0)] \end{align} \]

We can only calculate

\[ E[Y_i(1) | D_i = 1] - E[Y_i(0) | D_i = 0] \]

We need to convince ourselves that

\[ E[Y_i(1)] - E[Y_i(0)] = E[Y_i(1) | D_i = 1] - E[Y_i(0) | D_i = 0] \]

ATE decomposition

\[ \begin{align} E[\tau_i] & = E[Y_i(1) - Y_i(0)] \\ & = E[Y_i(1)] - E[Y_i(0)] \end{align} \]

We can only calculate

\[ E[Y_i(1) | D_i = 1] - E[Y_i(0) | D_i = 0] \]

We need to convince ourselves that

\[ E[Y_i(1)] - E[Y_i(0)] = E[Y_i(1) \color{purple}{| D_i = 1}] - E[Y_i(0) \color{purple}{| D_i = 0}] \]

ATE decomposition

\[ \begin{align} E[\tau_i] & = E[Y_i(1) - Y_i(0)] \\ & = E[Y_i(1)] - E[Y_i(0)] \end{align} \]

We can only calculate

\[ E[Y_i(1) | D_i = 1] - E[Y_i(0) | D_i = 0] \]

We need to convince ourselves that \(D_i\) can be ignored

\[ E[Y_i(1)] - E[Y_i(0)] = E[Y_i(1) \color{purple}{| D_i = 1}] - E[Y_i(0) \color{purple}{| D_i = 0}] \]

Obstacle

\[ E[Y_i(1) | D_i = 1] - E[Y_i(0) | D_i = 0] \]

Obstacle

\[ E[\color{purple}{Y_i(1)} | D_i = 1] - E[Y_i(0) | D_i = 0] \]

Rewrite to include \(\tau_i\)

\[ = E[\color{purple}{\tau_i + Y_i(0)} | D_i = 1] - E[Y_i(0) | D_i = 0] \]

Apply linearity of expectations again

\[ = E[\color{purple}{\tau_i} | D_i = 1] + E[\color{purple}{Y_i(0)} | D_i = 1] - E[Y_i(0) | D_i = 0] \]

Obstacle

\[ E[\color{purple}{Y_i(1)} | D_i = 1] - E[Y_i(0) | D_i = 0] \]

Rewrite to include \(\tau_i\)

\[ = E[\color{purple}{\tau_i + Y_i(0)} | D_i = 1] - E[Y_i(0) | D_i = 0] \]

Apply linearity of expectations again

\[ = \underbrace{E[\color{purple}{\tau_i} | D_i = 1]}_{\text{ATE on the treated (ATT)}} + \underbrace{E[\color{purple}{Y_i(0)} | D_i = 1] - E[Y_i(0) | D_i = 0]}_{\text{Selection bias}} \]

We want to eliminate selection bias

How?

Strategy 1: Random assignment

If treatment \(D_i\) is randomly assigned

• Potential outcomes are independent from treatment: \((Y_i(0), Y_i(1)) \perp \!\!\! \perp D_i\)
• Positivity: \(0 < \text{Pr}[D_i = 1] < 1\)
• ATE \(E[\tau_i]\) is point-identified
• Estimate with difference in means between treatment and control: \(\widehat E_{DM}[\tau_i] = \widehat E[Y_i(1)] - \widehat E[Y_i(0)]\)

difference_in_means(Y ~ D, data = data) # estimatr package

Randomization inference

1. Choose a test statistic and sharp null hypothesis

2. Calculate observed test statistic \(T^{obs}\)

3. Randomly shuffle treatment assignment

4. Calculate test statistic \(\widetilde T_1\)

5. Repeat \(K\) times to obtain distribution of test statistics \(\widetilde T = \{\widetilde T_1, \ldots, \widetilde T_K \}\)

6. p-value: Proportion in \(\widetilde T >= T^{obs}\)

The sharp null hypothesis assumes no effect at all. \(H_0 : \tau_i = Y_i(1) - Y_i(0) = 0 \forall i\)

Example

experiment

     ID           Y D
1   001  0.73452088 1
2   002  0.77074300 0
3   003  0.43603904 1
4   004 -0.08670346 0
5   005  0.68140405 0
6   006  1.97004908 0
7   007  0.03467949 0
8   008 -0.15014153 0
9   009  1.93785072 1
10  010  1.03405589 1
11  011 -0.63776244 0
12  012 -0.02706806 1
13  013  1.07300224 1
14  014 -1.93937350 1
15  015  0.02790501 1
16  016 -0.35149453 0
17  017  0.54079046 0
18  018  1.44996706 0
19  019  0.73112967 1
20  020  0.79690824 0
21  021 -0.27269854 0
22  022 -0.27808426 1
23  023  0.51189702 0
24  024  1.36787778 0
25  025 -0.53588199 0
26  026 -0.97449045 1
27  027 -0.30534497 1
28  028  0.78755569 0
29  029  1.29057502 0
30  030 -0.29850392 0
31  031  1.35695956 1
32  032  1.66123394 1
33  033 -0.10080816 1
34  034  2.22298971 1
35  035  0.37412061 0
36  036  0.96894977 0
37  037 -0.73311578 1
38  038  3.80851080 0
39  039  0.28927338 1
40  040  2.08703325 1
41  041  0.54731664 0
42  042  0.75394287 0
43  043  0.09015847 1
44  044 -0.90991412 0
45  045 -0.03775686 1
46  046 -0.01659609 0
47  047  1.40690978 1
48  048 -0.01060873 1
49  049  0.01867026 1
50  050  0.76318358 1
51  051 -0.79504822 0
52  052 -0.55555399 0
53  053 -1.33573394 0
54  054  0.32093037 0
55  055 -0.46741037 1
56  056  0.18678302 0
57  057  1.12459600 0
58  058 -0.07427236 1
59  059 -0.08427221 1
60  060  1.09717098 1
61  061 -0.63543347 0
62  062  0.33663997 0
63  063  0.36397851 0
64  064 -0.86762819 1
65  065  0.63749833 1
66  066  0.03136840 1
67  067 -0.50679316 0
68  068  1.45469951 1
69  069  1.05952630 0
70  070 -0.07452616 0
71  071 -0.58036503 1
72  072 -0.21894114 1
73  073  1.59581402 1
74  074 -0.32160300 0
75  075 -0.64248143 0
76  076  0.24132506 1
77  077 -1.54571192 0
78  078  1.42652245 1
79  079  0.13653512 1
80  080 -0.15238495 0
81  081  0.61609104 0
82  082 -0.19122112 1
83  083  0.91385643 1
84  084 -0.28182279 0
85  085 -0.85947519 0
86  086 -0.69182843 0
87  087 -0.47407936 0
88  088  0.58345214 1
89  089  1.65531353 1
90  090 -0.79963168 0
91  091 -0.52715729 1
92  092  0.39807853 1
93  093  0.41642051 1
94  094 -1.09120280 1
95  095  0.17952844 1
96  096 -1.83358910 0
97  097  1.15446368 1
98  098  0.44128714 1
99  099  1.47267069 0
100 100  0.06886880 0

Create randomization distribution

• Code
• Output

set.seed(20241108)

null_df = experiment %>% 
  specify(Y ~ D) %>% 
  hypothesize(null = "independence") %>% 
  generate(reps = 1000, type = "permute") %>% 
  split(.$replicate) %>% 
  map(~difference_in_means(Y ~ D, data = .)) %>% 
  map(tidy) %>% 
  bind_rows(.id = "replicate")

     replicate term      estimate std.error     statistic     p.value
1            1    D  0.1153412268 0.1878193  0.6141073101 0.540573797
2            2    D -0.1826480966 0.1872737 -0.9753002555 0.332012531
3            3    D  0.2955517522 0.1857970  1.5907241794 0.114984414
4            4    D -0.0668328670 0.1880592 -0.3553820001 0.723071275
5            5    D  0.2622549322 0.1863063  1.4076545925 0.162397711
6            6    D  0.1611433858 0.1874750  0.8595459148 0.392172528
7            7    D  0.1017260419 0.1878996  0.5413850878 0.589571462
8            8    D -0.0279077043 0.1881593 -0.1483195916 0.882395417
9            9    D -0.1205967677 0.1877856 -0.6422043886 0.522313453
10          10    D  0.2249861257 0.1868029  1.2044036039 0.231334398
11          11    D  0.0111052940 0.1881770  0.0590151406 0.953066314
12          12    D -0.3259859333 0.1852768 -1.7594534571 0.081714278
13          13    D  0.1675767012 0.1874175  0.8941360314 0.373624078
14          14    D -0.1554821756 0.1875238 -0.8291330552 0.409057329
15          15    D -0.2242053566 0.1868125 -1.2001624229 0.232983652
16          16    D -0.1361690588 0.1876770 -0.7255501312 0.469933582
17          17    D -0.1545070202 0.1875320 -0.8238967521 0.412047883
18          18    D  0.2187984315 0.1868779  1.1708094455 0.244515455
19          19    D  0.1799442922 0.1873004  0.9607255307 0.339186460
20          20    D -0.0142672792 0.1881749 -0.0758192647 0.939722266
21          21    D -0.0023951847 0.1881802 -0.0127281426 0.989871318
22          22    D  0.1278327399 0.1877368  0.6809146571 0.497551454
23          23    D  0.0674356898 0.1880570  0.3585916815 0.720770705
24          24    D  0.0404156883 0.1881361  0.2148215669 0.830353599
25          25    D -0.3547861433 0.1847361 -1.9205023223 0.058301550
26          26    D  0.1320541191 0.1877070  0.7035120167 0.483407490
27          27    D  0.1677531492 0.1874158  0.8950851945 0.373065225
28          28    D  0.0666607318 0.1880599  0.3544655007 0.723813831
29          29    D  0.1726545544 0.1873704  0.9214611071 0.359200407
30          30    D -0.0793481629 0.1880096 -0.4220431583 0.673920037
31          31    D -0.1296072153 0.1877244 -0.6904122462 0.491583964
32          32    D  0.0533549863 0.1881032  0.2836474488 0.777290271
33          33    D -0.0375219099 0.1881422 -0.1994337788 0.842348788
34          34    D -0.2641900978 0.1862784 -1.4182539992 0.159299447
35          35    D -0.1221630750 0.1877753 -0.6505811126 0.516912825
36          36    D  0.0598267303 0.1880833  0.3180863354 0.751097054
37          37    D -0.0619667999 0.1880762 -0.3294770284 0.742511121
38          38    D  0.1682873113 0.1874110  0.8979587515 0.371484367
39          39    D -0.0278088028 0.1881594 -0.1477938476 0.882810423
40          40    D  0.0803134396 0.1880054  0.4271868498 0.670193955
41          41    D -0.3733916212 0.1843616 -2.0253224543 0.045745216
42          42    D -0.0841410631 0.1879883 -0.4475866333 0.655480471
43          43    D  0.3074203062 0.1856004  1.6563561851 0.101218395
44          44    D -0.1769068587 0.1873299 -0.9443597686 0.347347190
45          45    D -0.1642876295 0.1874472 -0.8764476426 0.383033209
46          46    D -0.0623282683 0.1880750 -0.3314011009 0.741078908
47          47    D -0.0613653298 0.1880783 -0.3262755251 0.744912490
48          48    D -0.0932679240 0.1879444 -0.4962527998 0.620830229
49          49    D -0.0539113345 0.1881016 -0.2866075911 0.775032449
50          50    D  0.0635588234 0.1880708  0.3379515468 0.736137859
51          51    D -0.1161411557 0.1878143 -0.6183829054 0.537827653
52          52    D  0.1248537843 0.1877573  0.6649744782 0.507727947
53          53    D -0.1517165512 0.1875553 -0.8089165188 0.420685306
54          54    D -0.2563627286 0.1863900 -1.3754105029 0.172140793
55          55    D -0.2824650274 0.1860046 -1.5185917411 0.132443367
56          56    D  0.0548065878 0.1880989  0.2913710949 0.771411820
57          57    D  0.2790049733 0.1860579  1.4995602140 0.137179645
58          58    D  0.0235251099 0.1881654  0.1250235893 0.900762201
59          59    D -0.2318957099 0.1867167 -1.2419656113 0.217261577
60          60    D  0.0905554253 0.1879579  0.4817856483 0.631046649
61          61    D -0.5035856373 0.1811743 -2.7795649665 0.006725205
62          62    D -0.2319067976 0.1867166 -1.2420259286 0.217311321
63          63    D -0.1669423055 0.1874232 -0.8907236412 0.375318661
64          64    D  0.2543662439 0.1864179  1.3644948595 0.175543018
65          65    D  0.2384262418 0.1866327  1.2775155920 0.204462124
66          66    D -0.3868883969 0.1840774 -2.1017705044 0.038205356
67          67    D -0.1041345613 0.1878861 -0.5542429198 0.580675694
68          68    D -0.2979368330 0.1857581 -1.6038967921 0.112105133
69          69    D -0.0563216820 0.1880944 -0.2994331388 0.765250326
70          70    D  0.2527161013 0.1864408  1.3554765049 0.178477362
71          71    D -0.0674049402 0.1880572 -0.3584279551 0.720811342
72          72    D -0.1670487340 0.1874223 -0.8912960940 0.374994788
73          73    D  0.0596402439 0.1880839  0.3170938070 0.751859597
74          74    D -0.0546999448 0.1880992 -0.2908036535 0.771816262
75          75    D  0.2048137968 0.1870396  1.0950291528 0.276193417
76          76    D -0.0801218863 0.1880062 -0.4261660881 0.670943519
77          77    D  0.3308682547 0.1851885  1.7866567616 0.077409327
78          78    D  0.4175200553 0.1833932  2.2766393095 0.025013324
79          79    D  0.0311804541 0.1881540  0.1657177190 0.868722740
80          80    D  0.1653957366 0.1874372  0.8824060238 0.379783223
81          81    D -0.1215843506 0.1877792 -0.6474858917 0.518880884
82          82    D  0.3851074139 0.1841155  2.0916623410 0.039141347
83          83    D  0.1135260783 0.1878306  0.6044066639 0.546993153
84          84    D -0.1218559597 0.1877774 -0.6489385287 0.518020776
85          85    D -0.1215504808 0.1877794 -0.6473047503 0.518948384
86          86    D -0.1600224776 0.1874848 -0.8535223382 0.395548806
87          87    D  0.0074699045 0.1881789  0.0396957684 0.968416616
88          88    D  0.2277930860 0.1867682  1.2196565828 0.225522598
89          89    D  0.2684913623 0.1862156  1.4418303287 0.152548597
90          90    D  0.3559145472 0.1847140  1.9268415429 0.056925270
91          91    D -0.0755612484 0.1880255 -0.4018669980 0.688664660
92          92    D -0.0311500673 0.1881541 -0.1655561746 0.868847307
93          93    D -0.3423288144 0.1849758 -1.8506680889 0.067373269
94          94    D  0.0748689655 0.1880283  0.3981791576 0.691370269
95          95    D  0.1451316428 0.1876084  0.7735880659 0.441113169
96          96    D  0.0873918104 0.1879732  0.4649163447 0.643050166
97          97    D  0.2053484400 0.1870336  1.0979227161 0.274931517
98          98    D -0.1291998977 0.1877273 -0.6882319790 0.492937991
99          99    D  0.0710205716 0.1880436  0.3776814634 0.706533612
100        100    D -0.0816945451 0.1879993 -0.4345469791 0.664850422
101        101    D -0.1311338243 0.1877136 -0.6985846891 0.486504532
102        102    D  0.2469548229 0.1865195  1.3240157922 0.188581000
103        103    D  0.2986198875 0.1857469  1.6076707752 0.111240994
104        104    D  0.0929681305 0.1879459  0.4946536924 0.621951956
105        105    D  0.1851593228 0.1872485  0.9888425235 0.325274211
106        106    D -0.3477073468 0.1848734 -1.8807861808 0.063050321
107        107    D  0.0984996912 0.1879171  0.5241655489 0.601351416
108        108    D -0.0523515012 0.1881061 -0.2783084332 0.781434966
109        109    D -0.2757815567 0.1861069 -1.4818448942 0.141596119
110        110    D -0.1894422457 0.1872048 -1.0119517342 0.314087538
111        111    D  0.2221667928 0.1868374  1.1890918956 0.237404397
112        112    D -0.1608331634 0.1874777 -0.8578787356 0.393447053
113        113    D -0.0997348392 0.1879105 -0.5307571581 0.596826640
114        114    D  0.1361040904 0.1876775  0.7252021020 0.470057383
115        115    D  0.0520328409 0.1881070  0.2766130608 0.782699854
116        116    D  0.1501065345 0.1875685  0.8002758914 0.425525742
117        117    D -0.1817790581 0.1872823 -0.9706150659 0.334150989
118        118    D  0.0731611180 0.1880352  0.3890820368 0.698065087
119        119    D  0.3125074159 0.1855136  1.6845521457 0.095480828
120        120    D -0.0432054941 0.1881298 -0.2296579482 0.818844535
121        121    D  0.0309773050 0.1881544  0.1646377239 0.869572450
122        122    D  0.3181917246 0.1854150  1.7161053937 0.089344238
123        123    D -0.3460494101 0.1849051 -1.8714969158 0.064300944
124        124    D -0.0989195022 0.1879149 -0.5264058743 0.599818402
125        125    D -0.0294939418 0.1881568 -0.1567519407 0.875766944
126        126    D -0.0927777745 0.1879469 -0.4936383481 0.622742162
127        127    D  0.1595222538 0.1874892  0.8508345218 0.396947488
128        128    D -0.2177635068 0.1868903 -1.1651945662 0.247142847
129        129    D -0.1305685004 0.1877176 -0.6955581583 0.488472500
130        130    D  0.2651138279 0.1862650  1.4233151937 0.157930890
131        131    D -0.0584509715 0.1880877 -0.3107644176 0.756640699
132        132    D -0.0538269654 0.1881018 -0.2861586863 0.775372036
133        133    D  0.0838192466 0.1879898  0.4458712580 0.656719459
134        134    D  0.2838724897 0.1859827  1.5263379819 0.130171913
135        135    D  0.1025684060 0.1878949  0.5458817179 0.586441677
136        136    D  0.1976945881 0.1871177  1.0565251340 0.293335136
137        137    D  0.1086349403 0.1878601  0.5782756476 0.564469838
138        138    D  0.2244002645 0.1868101  1.2012211121 0.232585223
139        139    D  0.4397380767 0.1828625  2.4047471245 0.018090371
140        140    D  0.0529112184 0.1881045  0.2812863636 0.779084091
141        141    D -0.1420724837 0.1876323 -0.7571855515 0.450861540
142        142    D -0.0724749048 0.1880379 -0.3854270918 0.700763441
143        143    D -0.1154646583 0.1878186 -0.6147670253 0.540134731
144        144    D -0.0870227114 0.1879749 -0.4629484687 0.644495711
145        145    D  0.2625793623 0.1863016  1.4094312489 0.161920669
146        146    D -0.1656051161 0.1874353 -0.8835319804 0.379239718
147        147    D -0.0920661979 0.1879504 -0.4898429905 0.625343740
148        148    D -0.2574182962 0.1863751 -1.3811837339 0.170382093
149        149    D -0.0341713572 0.1881487 -0.1816188720 0.856258468
150        150    D -0.0566884195 0.1880932 -0.3013846930 0.763775258
151        151    D -0.1639309230 0.1874504 -0.8745298046 0.383977619
152        152    D -0.0152704422 0.1881741 -0.0811506259 0.935494702
153        153    D  0.2097527934 0.1869837  1.1217703358 0.264730208
154        154    D -0.0626928358 0.1880738 -0.3333417076 0.739618463
155        155    D  0.0542357453 0.1881006  0.2883337074 0.773718020
156        156    D  0.1515886187 0.1875563  0.8082298645 0.420954043
157        157    D -0.0568384117 0.1880928 -0.3021828706 0.763154209
158        158    D -0.0780323115 0.1880152 -0.4150319002 0.679045626
159        159    D  0.3066020136 0.1856142  1.6518243683 0.101777445
160        160    D -0.0196386978 0.1881699 -0.1043668297 0.917113084
161        161    D  0.0969513918 0.1879254  0.5159037264 0.607133050
162        162    D -0.0911480108 0.1879550 -0.4849459454 0.628824005
163        163    D  0.3210471019 0.1853648  1.7319745423 0.086740588
164        164    D  0.0894349553 0.1879634  0.4758105089 0.635360302
165        165    D  0.0084913115 0.1881784  0.0451237263 0.964100952
166        166    D -0.0315470062 0.1881534 -0.1676664239 0.867200476
167        167    D  0.2834053713 0.1859900  1.5237668027 0.130874098
168        168    D -0.2799271131 0.1860437 -1.5046307144 0.135669994
169        169    D -0.1142735529 0.1878260 -0.6084011595 0.544331691
170        170    D -0.1897120499 0.1872020 -1.0134080515 0.313563588
171        171    D -0.2755625805 0.1861102 -1.4806419468 0.142300194
172        172    D  0.1714743761 0.1873815  0.9151084607 0.362381375
173        173    D  0.0511591331 0.1881094  0.2719647856 0.786221914
174        174    D  0.0740573838 0.1880316  0.3938560145 0.694584391
175        175    D -0.0245373880 0.1881641 -0.1304042290 0.896519209
176        176    D  0.1615454687 0.1874715  0.8617068724 0.390984442
177        177    D -0.0098289004 0.1881778 -0.0522319993 0.958450498
178        178    D  0.0388071230 0.1881395  0.2062677684 0.837014478
179        179    D -0.1046118490 0.1878834 -0.5567912403 0.578944187
180        180    D  0.1421070923 0.1876321  0.7573710799 0.450718418
181        181    D -0.0128891877 0.1881759 -0.0684954324 0.945531430
182        182    D -0.0617345653 0.1880770 -0.3282408785 0.743436292
183        183    D -0.2310207206 0.1867278 -1.2372060893 0.218974410
184        184    D -0.1942973888 0.1871540 -1.0381682870 0.301844448
185        185    D -0.0350007377 0.1881472 -0.1860285217 0.852861872
186        186    D -0.2199804347 0.1868638 -1.1772236482 0.241979478
187        187    D -0.3347657360 0.1851170 -1.8084008805 0.074076659
188        188    D  0.0415137908 0.1881336  0.2206611743 0.825841174
189        189    D  0.1479299978 0.1875861  0.7885977524 0.432263540
190        190    D -0.0244250432 0.1881642 -0.1298070686 0.896986481
191        191    D  0.0216617151 0.1881677  0.1151192286 0.908626791
192        192    D -0.0268257365 0.1881609 -0.1425680982 0.886928342
193        193    D  0.0029670972 0.1881801  0.0157673241 0.987452473
194        194    D -0.1608482350 0.1874776 -0.8579597308 0.393173622
195        195    D -0.3544042203 0.1847436 -1.9183572468 0.057979760
196        196    D  0.1204136652 0.1877868  0.6412252335 0.522934544
197        197    D -0.1616069507 0.1874709 -0.8620373125 0.390772857
198        198    D -0.1163970103 0.1878127 -0.6197505130 0.536898495
199        199    D  0.0465789065 0.1881215  0.2476000661 0.804961922
200        200    D  0.0070717217 0.1881790  0.0375797565 0.970113520
201        201    D -0.0613811380 0.1880782 -0.3263596675 0.744851760
202        202    D -0.2092436056 0.1869895 -1.1190123313 0.265991758
203        203    D -0.0376008290 0.1881420 -0.1998534145 0.842037036
204        204    D  0.0634593852 0.1880712  0.3374222046 0.736529793
205        205    D  0.1996500849 0.1870965  1.0670965843 0.288582304
206        206    D  0.1461478939 0.1876004  0.7790383675 0.437925989
207        207    D -0.0826881144 0.1879949 -0.4398423113 0.661104863
208        208    D  0.1196559792 0.1877918  0.6371736459 0.525497491
209        209    D -0.0254555624 0.1881628 -0.1352847726 0.892671437
210        210    D  0.0390337466 0.1881391  0.2074728464 0.836071347
211        211    D -0.1902666190 0.1871963 -1.0164016431 0.311952221
212        212    D -0.1400464726 0.1876479 -0.7463259614 0.457285401
213        213    D -0.1543286888 0.1875335 -0.8229392384 0.412546905
214        214    D -0.0237887881 0.1881650 -0.1264251272 0.899677937
215        215    D -0.3754941400 0.1843180 -2.0372083313 0.044464889
216        216    D  0.1038558896 0.1878877  0.5527550945 0.581698993
217        217    D -0.0728123074 0.1880366 -0.3872241636 0.699434818
218        218    D -0.2432925785 0.1865686 -1.3040378370 0.195840321
219        219    D -0.0043333368 0.1881799 -0.0230276322 0.981677639
220        220    D  0.2278485115 0.1867675  1.2199578504 0.225450452
221        221    D  0.5205984710 0.1806829  2.8812822457 0.004897791
222        222    D  0.1840528398 0.1872597  0.9828749294 0.328158002
223        223    D  0.2616885437 0.1863144  1.4045532339 0.163316589
224        224    D  0.3092386277 0.1855695  1.6664299309 0.098873403
225        225    D -0.0257343276 0.1881624 -0.1367665643 0.891506093
226        226    D  0.0540753077 0.1881011  0.2874800520 0.774351955
227        227    D  0.0025634968 0.1881802  0.0136225642 0.989163175
228        228    D  0.1150560343 0.1878211  0.6125830482 0.541577881
229        229    D  0.2702873898 0.1861891  1.4516819072 0.149784528
230        230    D  0.3216639377 0.1853539  1.7354043901 0.085814511
231        231    D  0.1818493271 0.1872816  0.9709938783 0.334044868
232        232    D -0.1301512058 0.1877205 -0.6933242452 0.489763015
233        233    D  0.2307979513 0.1867306  1.2359944662 0.219458355
234        234    D  0.1778393919 0.1873209  0.9493834569 0.344822710
235        235    D -0.0188876021 0.1881707 -0.1003748289 0.920263935
236        236    D -0.0706870049 0.1880449 -0.3759050199 0.707800030
237        237    D -0.1804233418 0.1872957 -0.9633073705 0.337806289
238        238    D  0.1382391742 0.1876615  0.7366409515 0.463277131
239        239    D  0.0610603419 0.1880793  0.3246521756 0.746145304
240        240    D -0.1707120480 0.1873886 -0.9110056083 0.364542517
241        241    D  0.1968900129 0.1871264  1.0521766257 0.295480072
242        242    D -0.1804949759 0.1872950 -0.9636934595 0.337587679
243        243    D  0.0123898284 0.1881762  0.0658416288 0.947638044
244        244    D -0.1781865588 0.1873176 -0.9512538795 0.343829442
245        245    D  0.1070505924 0.1878694  0.5698138411 0.570114804
246        246    D -0.0504859509 0.1881113 -0.2683834639 0.788994766
247        247    D -0.0736248204 0.1880334 -0.3915519232 0.696245699
248        248    D -0.0991531451 0.1879136 -0.5276527465 0.598942278
249        249    D -0.1216848165 0.1877785 -0.6480232050 0.518493630
250        250    D  0.1870373013 0.1872295  0.9989734714 0.320319333
251        251    D -0.2001141732 0.1870915 -1.0696059824 0.287473934
252        252    D -0.1218667051 0.1877773 -0.6489959989 0.517899877
253        253    D -0.1185724537 0.1877988 -0.6313802441 0.529553443
254        254    D -0.1291729305 0.1877274 -0.6880876335 0.493044518
255        255    D -0.1337073122 0.1876950 -0.7123646468 0.478017771
256        256    D  0.0236431655 0.1881652  0.1256510932 0.900269424
257        257    D -0.0651093428 0.1880654 -0.3462058483 0.729941077
258        258    D  0.2264566639 0.1867848  1.2123934251 0.228278682
259        259    D  0.1728666184 0.1873684  0.9226027216 0.358483229
260        260    D -0.3796337442 0.1842314 -2.0606349556 0.042010559
261        261    D -0.2111964308 0.1869671 -1.1295911701 0.261430954
262        262    D -0.0022927783 0.1881802 -0.0121839486 0.990305804
263        263    D -0.2393792475 0.1866203 -1.2827074646 0.202710382
264        264    D -0.1872117368 0.1872277 -0.9999146392 0.319852920
265        265    D -0.0484702277 0.1881167 -0.2576604634 0.797220417
266        266    D -0.2122046010 0.1869555 -1.1350541204 0.259126186
267        267    D -0.0054178074 0.1881796 -0.0287906235 0.977091701
268        268    D -0.0365182248 0.1881442 -0.1940969841 0.846518747
269        269    D  0.1830839958 0.1872694  0.9776505345 0.330654560
270        270    D  0.0613568603 0.1880783  0.3262304442 0.744955614
271        271    D  0.1636972697 0.1874524  0.8732736168 0.384763321
272        272    D  0.2965416220 0.1857809  1.5961901484 0.113986237
273        273    D -0.2764083387 0.1860974 -1.4852884805 0.140772416
274        274    D  0.1451649924 0.1876082  0.7737669134 0.441022438
275        275    D -0.4636967316 0.1822576 -2.5441834783 0.012669591
276        276    D  0.0460324609 0.1881229  0.2446935331 0.807238128
277        277    D -0.0182798902 0.1881713 -0.0971449350 0.922815035
278        278    D -0.0823457260 0.1879964 -0.4380174737 0.662384946
279        279    D -0.0026702384 0.1881802 -0.0141897958 0.988707566
280        280    D  0.3494852502 0.1848392  1.8907529395 0.061718624
281        281    D  0.0331670005 0.1881505  0.1762790534 0.860444250
282        282    D  0.2983454281 0.1857514  1.6061542619 0.111643177
283        283    D  0.1240433625 0.1877627  0.6606388649 0.510474332
284        284    D -0.1138592204 0.1878286 -0.6061869350 0.545806247
285        285    D -0.3301123429 0.1852022 -1.7824424233 0.077785712
286        286    D -0.0476061570 0.1881189 -0.2530641638 0.800749258
287        287    D -0.0011753817 0.1881803 -0.0062460387 0.995029121
288        288    D -0.2008895985 0.1870830 -1.0737992838 0.285622587
289        289    D  0.1839190715 0.1872610  0.9821535488 0.328525486
290        290    D  0.0316399412 0.1881532  0.1681604985 0.866835739
291        291    D  0.0671234917 0.1880582  0.3569293939 0.721934890
292        292    D  0.0549054695 0.1880986  0.2918972415 0.770986277
293        293    D -0.1658918688 0.1874328 -0.8850740744 0.378283605
294        294    D -0.0214431982 0.1881679 -0.1139577856 0.909510254
295        295    D -0.2312452384 0.1867249 -1.2384272775 0.218523048
296        296    D  0.1295482415 0.1877248  0.6900965686 0.491820604
297        297    D  0.1822102887 0.1872781  0.9729398500 0.333255188
298        298    D  0.1553526422 0.1875249  0.8284374586 0.409475072
299        299    D -0.0069430313 0.1881791 -0.0368958748 0.970645011
300        300    D -0.0387848517 0.1881396 -0.2061493406 0.837102147
301        301    D  0.2657009472 0.1862565  1.4265326375 0.157149854
302        302    D  0.0264072460 0.1881615  0.1403435372 0.888683551
303        303    D -0.2224019131 0.1868345 -1.1903685036 0.236780600
304        304    D  0.2676933135 0.1862274  1.4374542149 0.154004834
305        305    D  0.2086385788 0.1869964  1.1157355516 0.267427447
306        306    D  0.2929190767 0.1858395  1.5761936759 0.118519608
307        307    D -0.0950453613 0.1879353 -0.5057345023 0.614201956
308        308    D -0.3524340569 0.1847821 -1.9072959254 0.059476408
309        309    D  0.2221637796 0.1868374  1.1890755355 0.237337210
310        310    D -0.3774629040 0.1842769 -2.0483457388 0.043202820
311        311    D  0.1423806677 0.1876299  0.7588376810 0.449857470
312        312    D  0.1319425752 0.1877078  0.7029147746 0.483879177
313        313    D  0.0738359758 0.1880325  0.3926766553 0.695414708
314        314    D -0.1244888369 0.1877597 -0.6630220274 0.509049042
315        315    D -0.2203644714 0.1868591 -1.1793079579 0.241137977
316        316    D  0.2661703319 0.1862496  1.4291052080 0.156216063
317        317    D -0.1063780629 0.1878733 -0.5662223220 0.572556385
318        318    D  0.1048867090 0.1878819  0.5582588149 0.577952801
319        319    D  0.0057397847 0.1881795  0.0305016500 0.975729066
320        320    D  0.3029393690 0.1856755  1.6315524757 0.106227500
321        321    D  0.3634329808 0.1845645  1.9691378276 0.051809236
322        322    D -0.1931298127 0.1871664 -1.0318617160 0.304684641
323        323    D  0.1771632278 0.1873275  0.9457407929 0.346750276
324        324    D  0.2597340960 0.1863423  1.3938544231 0.166528892
325        325    D -0.0667118835 0.1880597 -0.3547378468 0.723548583
326        326    D  0.1272118928 0.1877411  0.6775921181 0.499704815
327        327    D  0.2083731764 0.1869995  1.1142982667 0.267982977
328        328    D -0.1021398543 0.1878973 -0.5435940211 0.587956782
329        329    D -0.3892450743 0.1840267 -2.1151557651 0.037003809
330        330    D -0.0112135264 0.1881770 -0.0595903243 0.952610780
331        331    D  0.4295849804 0.1831086  2.3460666576 0.021059059
332        332    D  0.1821543574 0.1872786  0.9726383127 0.333405787
333        333    D  0.0558087960 0.1880959  0.2967039294 0.767323221
334        334    D  0.0932414294 0.1879445  0.4961114754 0.621089167
335        335    D -0.1239182240 0.1877636 -0.6599694299 0.510827861
336        336    D  0.2489581550 0.1864924  1.3349509074 0.185266875
337        337    D -0.0208983732 0.1881685 -0.1110619971 0.911817465
338        338    D -0.1054377696 0.1878787 -0.5612012324 0.576087111
339        339    D -0.0188979094 0.1881707 -0.1004296109 0.920251307
340        340    D -0.1658263941 0.1874333 -0.8847219601 0.378485182
341        341    D  0.1216970964 0.1877784  0.6480888810 0.518511606
342        342    D  0.0962455953 0.1879291  0.5121379097 0.609752390
343        343    D -0.1831746827 0.1872685 -0.9781395204 0.330416562
344        344    D  0.0701059470 0.1880471  0.3728106231 0.710170198
345        345    D -0.0051903718 0.1881796 -0.0275820044 0.978053811
346        346    D  0.1289733927 0.1877288  0.6870195980 0.493713033
347        347    D -0.3499668036 0.1848299 -1.8934534366 0.061346062
348        348    D  0.1925653296 0.1871723  1.0288131509 0.306109199
349        349    D  0.1648200643 0.1874424  0.8793104690 0.381415215
350        350    D -0.1228421868 0.1877708 -0.6542134830 0.514619550
351        351    D  0.3571162484 0.1846903  1.9335950507 0.056218484
352        352    D -0.2206779840 0.1868554 -1.1810096216 0.240548874
353        353    D  0.2983063839 0.1857521  1.6059385340 0.111609852
354        354    D -0.2701535027 0.1861911 -1.4509473635 0.150095331
355        355    D  0.1661018847 0.1874309  0.8862035349 0.377754969
356        356    D  0.1367830693 0.1876724  0.7288394597 0.467868680
357        357    D -0.1733651630 0.1873637 -0.9252867049 0.357296092
358        358    D  0.0262950641 0.1881616  0.1397472182 0.889182797
359        359    D  0.0732811459 0.1880347  0.3897213520 0.697594830
360        360    D  0.2742860700 0.1861294  1.4736307030 0.143788231
361        361    D  0.1130549502 0.1878335  0.6018891119 0.548702156
362        362    D -0.2477787085 0.1865084 -1.3285123633 0.187127765
363        363    D  0.1427731555 0.1876269  0.7609418420 0.448543366
364        364    D -0.1944990682 0.1871519 -1.0392577689 0.301376320
365        365    D -0.0397540887 0.1881375 -0.2113033497 0.833130251
366        366    D -0.1760451604 0.1873382 -0.9397183206 0.349693236
367        367    D  0.1035228309 0.1878896  0.5509769474 0.582914274
368        368    D  0.2503664831 0.1864731  1.3426410871 0.182544635
369        369    D -0.1457987179 0.1876032 -0.7771656072 0.439012565
370        370    D  0.0218499655 0.1881674  0.1161198056 0.907801573
371        371    D  0.2393433251 0.1866208  1.2825117445 0.202734139
372        372    D -0.3016490930 0.1856970 -1.6244158647 0.107500940
373        373    D -0.0596106990 0.1880840 -0.3169365621 0.751983731
374        374    D -0.0555518671 0.1880967 -0.2953367647 0.768373105
375        375    D  0.3102523206 0.1855523  1.6720481104 0.097916494
376        376    D  0.0469648054 0.1881206  0.2496526927 0.803402046
377        377    D -0.0943032881 0.1879391 -0.5017757610 0.616964785
378        378    D -0.2453342552 0.1865414 -1.3151734666 0.191527788
379        379    D  0.1513752790 0.1875581  0.8070848282 0.421610512
380        380    D -0.0237655286 0.1881651 -0.1263014949 0.899752160
381        381    D -0.2587513886 0.1863563 -1.3884768111 0.168191955
382        382    D -0.1685815227 0.1874083 -0.8995415749 0.370573363
383        383    D  0.2837651471 0.1859844  1.5257471052 0.130576269
384        384    D  0.0644421497 0.1880677  0.3426539104 0.732646648
385        385    D -0.3481630385 0.1848647 -1.8833402182 0.062638484
386        386    D  0.0839612455 0.1879891  0.4466281482 0.656179733
387        387    D -0.3322553837 0.1851631 -1.7943926949 0.075834047
388        388    D -0.0029630635 0.1881801 -0.0157458890 0.987469136
389        389    D -0.0563383570 0.1880943 -0.2995218723 0.765184135
390        390    D -0.0793184493 0.1880097 -0.4218848282 0.674124593
391        391    D -0.0630018588 0.1880727 -0.3349866786 0.738417770
392        392    D  0.0652413430 0.1880649  0.3469085940 0.729418818
393        393    D -0.0909505151 0.1879560 -0.4838926716 0.629554015
394        394    D -0.0450444086 0.1881254 -0.2394382635 0.811291200
395        395    D -0.2766052128 0.1860944 -1.4863702301 0.140455575
396        396    D  0.1592784167 0.1874913  0.8495243973 0.397673445
397        397    D -0.0107228582 0.1881773 -0.0569827532 0.954676333
398        398    D  0.2209657526 0.1868519  1.1825716447 0.239914581
399        399    D  0.1022399877 0.1878968  0.5441285458 0.587596308
400        400    D  0.1504129312 0.1875660  0.8019201187 0.424758663
401        401    D  0.0019254336 0.1881803  0.0102318564 0.991857638
402        402    D -0.2104556004 0.1869757 -1.1255774982 0.263214005
403        403    D  0.3051599126 0.1856384  1.6438402719 0.103618985
404        404    D  0.1185955510 0.1877987  0.6315037341 0.529378146
405        405    D -0.1393900696 0.1876529 -0.7428081627 0.459479445
406        406    D -0.0416874609 0.1881333 -0.2215847568 0.825098989
407        407    D -0.2030453027 0.1870593 -1.0854597888 0.280621726
408        408    D -0.0383111836 0.1881406 -0.2036306269 0.839081005
409        409    D -0.1169111509 0.1878094 -0.6224988316 0.535114285
410        410    D -0.3237313983 0.1853171 -1.7469047074 0.083791003
411        411    D -0.2162939585 0.1869077 -1.1572235844 0.249998457
412        412    D -0.3203213048 0.1853776 -1.7279396022 0.087300273
413        413    D -0.1086109119 0.1878603 -0.5781473057 0.564529625
414        414    D  0.0028781630 0.1881802  0.0152947213 0.987830839
415        415    D  0.0423346649 0.1881318  0.2250266567 0.822440780
416        416    D -0.1182390359 0.1878009 -0.6295976539 0.530423175
417        417    D  0.0926059648 0.1879477  0.4927219418 0.623394832
418        418    D -0.0273815211 0.1881600 -0.1455225037 0.884597342
419        419    D -0.0851564785 0.1879837 -0.4529993576 0.651584663
420        420    D  0.2424605776 0.1865797  1.2995013691 0.196856189
421        421    D  0.0575977474 0.1880904  0.3062237353 0.760091491
422        422    D  0.3913833493 0.1839804  2.1273101678 0.035920264
423        423    D -0.0732851288 0.1880347 -0.3897425668 0.697594768
424        424    D  0.1413441023 0.1876379  0.7532810549 0.453088112
425        425    D -0.2398660604 0.1866139 -1.2853599706 0.201711195
426        426    D -0.1040213579 0.1878868 -0.5536385236 0.581214265
427        427    D -0.1942636961 0.1871544 -1.0379862809 0.301909633
428        428    D  0.2038756355 0.1870500  1.0899523633 0.278733195
429        429    D  0.1682584372 0.1874112  0.8978034155 0.371491028
430        430    D  0.1445712970 0.1876128  0.7705831492 0.442808344
431        431    D  0.1537230682 0.1875386  0.8196876548 0.414401970
432        432    D  0.0345144087 0.1881481  0.1834427948 0.854835198
433        433    D  0.0885867428 0.1879675  0.4712875849 0.638485685
434        434    D  0.0887166065 0.1879669  0.4719800378 0.638066708
435        435    D  0.1710140648 0.1873858  0.9126310076 0.363724668
436        436    D  0.1741592355 0.1873562  0.9295621214 0.354898581
437        437    D -0.3145653231 0.1854782 -1.6959696540 0.093236357
438        438    D -0.0310452911 0.1881542 -0.1649991556 0.869287025
439        439    D -0.0264322614 0.1881614 -0.1404765107 0.888571841
440        440    D  0.0674670672 0.1880569  0.3587587508 0.720566337
441        441    D -0.0287120044 0.1881580 -0.1525951640 0.879036483
442        442    D  0.0463610013 0.1881221  0.2464410251 0.805891662
443        443    D -0.0128301791 0.1881759 -0.0681818355 0.945779973
444        444    D -0.2230356420 0.1868268 -1.1938096865 0.235441494
445        445    D -0.2220801915 0.1868384 -1.1886217003 0.237478645
446        446    D -0.1212216944 0.1877815 -0.6455463759 0.520092670
447        447    D  0.1326932328 0.1877024  0.7069341855 0.481410156
448        448    D -0.0097820261 0.1881778 -0.0519828963 0.958648521
449        449    D -0.1022509688 0.1878967 -0.5441871643 0.587564645
450        450    D  0.2244182820 0.1868099  1.2013189806 0.232853349
451        451    D  0.3666223469 0.1845001  1.9871114370 0.049867628
452        452    D  0.2255220140 0.1867963  1.2073149567 0.230285012
453        453    D -0.0249887953 0.1881634 -0.1328036662 0.894632571
454        454    D -0.2464726599 0.1865261 -1.3213846351 0.189621087
455        455    D  0.2410106954 0.1865989  1.2915978373 0.199541047
456        456    D -0.3701885010 0.1844275 -2.0072308300 0.047508311
457        457    D -0.5185038309 0.1807444 -2.8687136963 0.005053770
458        458    D -0.1446997494 0.1876118 -0.7712719706 0.442401656
459        459    D  0.1385179340 0.1876594  0.7381346407 0.462238450
460        460    D  0.1047870510 0.1878824  0.5577267013 0.578346019
461        461    D -0.2699557609 0.1861940 -1.4498625376 0.150339864
462        462    D  0.1607479315 0.1874785  0.8574207005 0.393369878
463        463    D -0.3009102696 0.1857092 -1.6203304896 0.108434321
464        464    D -0.1979129602 0.1871154 -1.0577054795 0.292790670
465        465    D  0.0447450389 0.1881261  0.2378460107 0.812497485
466        466    D -0.1438111151 0.1876188 -0.7665069282 0.445354335
467        467    D  0.0140034962 0.1881751  0.0744173871 0.940830160
468        468    D  0.2221229308 0.1868379  1.1888537491 0.237490475
469        469    D  0.1366822032 0.1876732  0.7282990913 0.468302665
470        470    D -0.0513833028 0.1881088 -0.2731573894 0.785325524
471        471    D  0.0599156426 0.1880830  0.3185595528 0.750744207
472        472    D  0.0018144820 0.1881803  0.0096422533 0.992326758
473        473    D -0.1189011682 0.1877967 -0.6331377487 0.528119112
474        474    D -0.1061420568 0.1878747 -0.5649620280 0.573512853
475        475    D -0.2376707166 0.1866426 -1.2734003085 0.206041203
476        476    D -0.1694541022 0.1874002 -0.9042363563 0.368093511
477        477    D -0.0154676915 0.1881739 -0.0821989259 0.934656683
478        478    D -0.1875004579 0.1872248 -1.0014724939 0.319123578
479        479    D -0.1169151899 0.1878094 -0.6225204224 0.535180381
480        480    D -0.1117193775 0.1878417 -0.5947528860 0.553384904
481        481    D  0.2535614077 0.1864291  1.3600958557 0.177312513
482        482    D -0.1098245523 0.1878531 -0.5846300473 0.560144246
483        483    D -0.1439603308 0.1876176 -0.7673070168 0.444744102
484        484    D -0.0649187112 0.1880661 -0.3451909685 0.730694029
485        485    D  0.2611734233 0.1863218  1.4017329547 0.164190813
486        486    D  0.0497040746 0.1881134  0.2642240226 0.792174898
487        487    D -0.1230767046 0.1877692 -0.6554679110 0.513755513
488        488    D  0.1273956620 0.1877398  0.6785755576 0.499025859
489        489    D  0.4607370043 0.1823342  2.5268825430 0.013109834
490        490    D -0.1134350929 0.1878312 -0.6039204589 0.547292331
491        491    D  0.4345856830 0.1829881  2.3749389511 0.019529430
492        492    D -0.0303666346 0.1881554 -0.1613912703 0.872132358
493        493    D -0.0252101749 0.1881631 -0.1339804090 0.893697117
494        494    D -0.0477714543 0.1881185 -0.2539434262 0.800077891
495        495    D -0.0697185248 0.1880485 -0.3707474849 0.711625868
496        496    D -0.0656134211 0.1880636 -0.3488894997 0.727921725
497        497    D  0.1925872124 0.1871721  1.0289313267 0.306177938
498        498    D -0.4249704454 0.1832184 -2.3194741685 0.022585442
499        499    D -0.0193074047 0.1881703 -0.1026060328 0.918486428
500        500    D -0.0589602142 0.1880861 -0.3134745951 0.754604372
501        501    D -0.0475725332 0.1881190 -0.2528853104 0.800886856
502        502    D  0.1788233581 0.1873114  0.9546850102 0.342173148
503        503    D  0.2655799700 0.1862582  1.4258696397 0.157132962
504        504    D  0.3677701399 0.1844768  1.9935844188 0.049140356
505        505    D  0.2102792445 0.1869777  1.1246221176 0.263518494
506        506    D -0.1523949568 0.1875497 -0.8125579304 0.418640760
507        507    D  0.0318855885 0.1881528  0.1694664500 0.865779144
508        508    D  0.3726172520 0.1843776  2.0209469407 0.046118057
509        509    D  0.0390881918 0.1881389  0.2077623618 0.835851725
510        510    D  0.2602064052 0.1863356  1.3964394432 0.165866815
511        511    D  0.1885987545 0.1872135  1.0073992564 0.316472141
512        512    D -0.0764837163 0.1880217 -0.4067813102 0.685112996
513        513    D -0.0088305044 0.1881783 -0.0469262729 0.962673437
514        514    D  0.0401479519 0.1881367  0.2133978037 0.831485338
515        515    D -0.1325725042 0.1877033 -0.7062877183 0.481788481
516        516    D -0.3229999756 0.1853302 -1.7428353627 0.084524503
517        517    D  0.3528630546 0.1847737  1.9097039103 0.059250490
518        518    D  0.2387450112 0.1866286  1.2792520978 0.203877457
519        519    D -0.1293575390 0.1877261 -0.6890757806 0.492421924
520        520    D  0.1354405691 0.1876824  0.7216478339 0.472263889
521        521    D  0.0176993424 0.1881719  0.0940594428 0.925254256
522        522    D -0.1872664774 0.1872272 -1.0002099975 0.319696811
523        523    D  0.0604742428 0.1880812  0.3215326373 0.748499242
524        524    D -0.0278053561 0.1881594 -0.1477755255 0.882824947
525        525    D  0.0100246608 0.1881777  0.0532723242 0.957631912
526        526    D -0.0769596860 0.1880197 -0.4093170862 0.683358926
527        527    D -0.1160002333 0.1878152 -0.6176296545 0.538253427
528        528    D -0.4159487099 0.1834296 -2.2676206597 0.025557070
529        529    D  0.0989300776 0.1879148  0.5264623110 0.599815663
530        530    D  0.2806525535 0.1860326  1.5086204514 0.134621104
531        531    D -0.3322307006 0.1851636 -1.7942550107 0.076078722
532        532    D  0.2046129704 0.1870418  1.0939423242 0.276917841
533        533    D -0.1299707426 0.1877218 -0.6923582003 0.490363737
534        534    D  0.2932374236 0.1858344  1.5779501955 0.118028083
535        535    D -0.1126185555 0.1878362 -0.5995572672 0.550213633
536        536    D  0.1916814754 0.1871816  1.0240403614 0.308535517
537        537    D  0.0548316132 0.1880988  0.2915042541 0.771301016
538        538    D  0.0390411694 0.1881390  0.2075123174 0.836040440
539        539    D  0.0060210517 0.1881794  0.0319963392 0.974541211
540        540    D -0.2544112181 0.1864173 -1.3647406989 0.175524797
541        541    D  0.1634686478 0.1874545  0.8720445198 0.385680100
542        542    D -0.1723882741 0.1873729 -0.9200276794 0.359829397
543        543    D  0.0787175391 0.1880123  0.4186829237 0.676364147
544        544    D -0.0329393455 0.1881510 -0.1750687118 0.861395945
545        545    D  0.3407465222 0.1850056  1.8418172274 0.068755703
546        546    D  0.2401451301 0.1866103  1.2868806657 0.201294063
547        547    D -0.1749379606 0.1873488 -0.9337554053 0.352811562
548        548    D -0.1076309102 0.1878660 -0.5729131014 0.568091670
549        549    D  0.4378490080 0.1829088  2.3938111474 0.018615760
550        550    D -0.5616352645 0.1794245 -3.1302045280 0.002324012
551        551    D  0.2609137621 0.1863255  1.4003114393 0.164581056
552        552    D  0.2281060305 0.1867643  1.2213576473 0.224887501
553        553    D  0.1165594229 0.1878117  0.6206186677 0.536338993
554        554    D -0.2267256387 0.1867815 -1.2138550878 0.227794774
555        555    D  0.0017998210 0.1881803  0.0095643438 0.992388961
556        556    D  0.3124584828 0.1855145  1.6842807385 0.095317749
557        557    D -0.3326439362 0.1851560 -1.7965601980 0.075614709
558        558    D  0.0777861127 0.1880163  0.4137201478 0.680024044
559        559    D -0.2198393243 0.1868655 -1.1764578283 0.242266720
560        560    D -0.1158943415 0.1878159 -0.6170636546 0.538624559
561        561    D  0.0355540932 0.1881461  0.1889706629 0.850537768
562        562    D -0.1452849153 0.1876072 -0.7744100435 0.440568545
563        563    D  0.1047681148 0.1878825  0.5576255940 0.578380389
564        564    D  0.0333285389 0.1881503  0.1771378872 0.859773249
565        565    D -0.0474334884 0.1881194 -0.2521456979 0.801468451
566        566    D -0.0819144985 0.1879984 -0.4357192116 0.664042118
567        567    D  0.1475311394 0.1875893  0.7864580463 0.433528679
568        568    D -0.1602116329 0.1874832 -0.8545387617 0.394993695
569        569    D  0.0109886771 0.1881771  0.0583954000 0.953558351
570        570    D -0.2886207934 0.1859081 -1.5524914898 0.123797405
571        571    D  0.1109739670 0.1878462  0.5907704149 0.556034575
572        572    D -0.0586697079 0.1880870 -0.3119285191 0.755793700
573        573    D -0.1923990325 0.1871741 -1.0279150971 0.306550232
574        574    D -0.0968244229 0.1879260 -0.5152262600 0.607631449
575        575    D  0.2455111425 0.1865390  1.3161384684 0.191615250
576        576    D -0.1348083137 0.1876870 -0.7182613056 0.474315004
577        577    D  0.2619085647 0.1863113  1.4057579491 0.163640129
578        578    D -0.0750499228 0.1880276 -0.3991431139 0.690661542
579        579    D -0.2596721378 0.1863432 -1.3935153375 0.166671414
580        580    D -0.4835432981 0.1817306 -2.6607704626 0.009111706
581        581    D -0.2937304950 0.1858265 -1.5806710669 0.117384837
582        582    D  0.1014378173 0.1879012  0.5398465915 0.590570462
583        583    D  0.0014406883 0.1881803  0.0076558925 0.993907585
584        584    D  0.2168580604 0.1869010  1.1602830679 0.248984533
585        585    D -0.0044355065 0.1881798 -0.0235705720 0.981243171
586        586    D -0.1773611236 0.1873256 -0.9468068670 0.346341838
587        587    D  0.1079185956 0.1878643  0.5744495836 0.566982260
588        588    D -0.0022058662 0.1881802 -0.0117220924 0.990671180
589        589    D -0.0924239004 0.1879486 -0.4917508522 0.623995743
590        590    D  0.0712731226 0.1880426  0.3790264736 0.705488803
591        591    D  0.1467319561 0.1875957  0.7821710962 0.436049933
592        592    D -0.0234496007 0.1881655 -0.1246222338 0.901080355
593        593    D  0.3763458362 0.1843003  2.0420255109 0.043858926
594        594    D  0.0989915385 0.1879145  0.5267903048 0.599530527
595        595    D  0.0809411743 0.1880027  0.4305320589 0.667754056
596        596    D  0.0444056804 0.1881269  0.2360410927 0.813894055
597        597    D  0.3118830596 0.1855244  1.6810894375 0.095977712
598        598    D -0.1885495828 0.1872140 -1.0071338872 0.316633082
599        599    D  0.3111804528 0.1855364  1.6771934653 0.096859864
600        600    D  0.0619162953 0.1880764  0.3292081983 0.742759308
601        601    D  0.2143270494 0.1869308  1.1465583376 0.254472735
602        602    D -0.2312203987 0.1867252 -1.2382921679 0.218723524
603        603    D -0.2956026280 0.1857962 -1.5910050762 0.114876578
604        604    D -0.1118153794 0.1878411 -0.5952658120 0.553068456
605        605    D  0.0816074699 0.1879997  0.4340829207 0.665233429
606        606    D  0.1018736387 0.1878988  0.5421729516 0.588939692
607        607    D  0.1800982153 0.1872989  0.9615550785 0.338818675
608        608    D  0.0770903345 0.1880192  0.4100131429 0.682703433
609        609    D -0.0228517224 0.1881662 -0.1214443423 0.903590466
610        610    D -0.3159993958 0.1854533 -1.7039299434 0.091608992
611        611    D -0.0342145839 0.1881486 -0.1818486971 0.856112739
612        612    D -0.0122861328 0.1881763 -0.0652905487 0.948091117
613        613    D -0.0245147830 0.1881641 -0.1302840736 0.896614010
614        614    D  0.3495177421 0.1848386  1.8909351379 0.061753761
615        615    D  0.0250004267 0.1881634  0.1328654927 0.894574246
616        616    D -0.1899668784 0.1871994 -1.0147835944 0.312735373
617        617    D -0.0319998695 0.1881526 -0.1700740131 0.865304762
618        618    D -0.0092004892 0.1881781 -0.0488924594 0.961108130
619        619    D  0.0745164904 0.1880298  0.3963015616 0.692749903
620        620    D  0.0237625261 0.1881651  0.1262855358 0.899765919
621        621    D  0.4271937142 0.1831657  2.3322803762 0.021954890
622        622    D  0.1434935407 0.1876213  0.7648041564 0.446252404
623        623    D -0.3347557294 0.1851172 -1.8083450212 0.073824416
624        624    D -0.0591781462 0.1880854 -0.3146344455 0.753709567
625        625    D -0.0615566165 0.1880776 -0.3272936942 0.744216435
626        626    D  0.3116506784 0.1855284  1.6798007936 0.096194535
627        627    D  0.0513923252 0.1881088  0.2732053899 0.785297344
628        628    D  0.1583056270 0.1874997  0.8442980876 0.400617823
629        629    D  0.0957648677 0.1879316  0.5095730876 0.611534834
630        630    D -0.1077207940 0.1878655 -0.5733931524 0.567748115
631        631    D  0.3953977045 0.1838928  2.1501535081 0.034139639
632        632    D  0.2356462049 0.1866688  1.2623761552 0.209809551
633        633    D  0.1873789812 0.1872260  1.0008170322 0.319481642
634        634    D -0.4904281704 0.1815422 -2.7014554865 0.008243091
635        635    D -0.1085932605 0.1878604 -0.5780530250 0.564634638
636        636    D  0.2729415990 0.1861496  1.4662485305 0.145926802
637        637    D -0.1362702100 0.1876762 -0.7260919941 0.469580937
638        638    D  0.0904864751 0.1879583  0.4814179418 0.631299831
639        639    D  0.0593015882 0.1880850  0.3152914188 0.753211009
640        640    D  0.1694289947 0.1874005  0.9041012610 0.368170456
641        641    D -0.1753852231 0.1873445 -0.9361640526 0.351490750
642        642    D -0.2424578453 0.1865797 -1.2994864730 0.196825849
643        643    D  0.3556668618 0.1847188  1.9254498847 0.057133256
644        644    D  0.2796542447 0.1860479  1.5031301932 0.136129808
645        645    D -0.2001872752 0.1870907 -1.0700012753 0.287426963
646        646    D  0.0183295773 0.1881713  0.0974090127 0.922602193
647        647    D -0.2070052651 0.1870150 -1.1068914519 0.271056826
648        648    D -0.0656936725 0.1880633 -0.3493167554 0.727656989
649        649    D -0.2252794652 0.1867993 -1.2059972088 0.230759512
650        650    D -0.1276977491 0.1877377 -0.6801922179 0.498015576
651        651    D  0.1124237371 0.1878374  0.5985163013 0.550914924
652        652    D -0.2089969752 0.1869924 -1.1176765561 0.266545749
653        653    D  0.0925104409 0.1879482  0.4922124377 0.623681646
654        654    D -0.1180741533 0.1878020 -0.6287161453 0.531056375
655        655    D -0.1459649477 0.1876018 -0.7780571488 0.438488550
656        656    D -0.0575308698 0.1880906 -0.3058678347 0.760411523
657        657    D -0.1934402088 0.1871631 -1.0335381746 0.303902523
658        658    D -0.1782187102 0.1873173 -0.9514271058 0.343805783
659        659    D  0.1452140015 0.1876078  0.7740297413 0.440829284
660        660    D  0.0449840019 0.1881255  0.2391169780 0.811574063
661        661    D -0.1020991816 0.1878975 -0.5433769061 0.588228548
662        662    D  0.0575977066 0.1880904  0.3062235185 0.760096873
663        663    D  0.0499754396 0.1881126  0.2656676197 0.791059468
664        664    D  0.1631887547 0.1874570  0.8705398376 0.386134365
665        665    D -0.0661637868 0.1880616 -0.3518196672 0.725729907
666        666    D -0.2183276329 0.1868835 -1.1682550375 0.245574827
667        667    D -0.2442572272 0.1865558 -1.3092985759 0.193807762
668        668    D  0.1930481139 0.1871672  1.0314204732 0.304964188
669        669    D -0.2199940584 0.1868636 -1.1772975862 0.241959976
670        670    D  0.0323272171 0.1881520  0.1718143327 0.863942539
671        671    D  0.0262706440 0.1881617  0.1396174100 0.889248819
672        672    D  0.0457546282 0.1881236  0.2432157712 0.808355192
673        673    D  0.0141003631 0.1881750  0.0749321868 0.940431648
674        674    D  0.1063583204 0.1878734  0.5661168939 0.572613966
675        675    D -0.0676601218 0.1880562 -0.3597866801 0.719827226
676        676    D -0.1713984348 0.1873822 -0.9146997236 0.362847137
677        677    D -0.2016230384 0.1870750 -1.0777660645 0.283783960
678        678    D  0.3021724305 0.1856883  1.6273101851 0.107083715
679        679    D -0.1007455515 0.1879050 -0.5361515458 0.593108538
680        680    D -0.0116444658 0.1881767 -0.0618804869 0.950784417
681        681    D  0.1132080922 0.1878326  0.6027074390 0.548131330
682        682    D  0.2590841684 0.1863516  1.3902977275 0.167588170
683        683    D -0.1599646443 0.1874853 -0.8532115772 0.395861404
684        684    D  0.0271766874 0.1881603  0.1444336567 0.885491660
685        685    D  0.2649306566 0.1862677  1.4223114959 0.158373268
686        686    D  0.0263607517 0.1881615  0.1400963901 0.888900135
687        687    D  0.1949824112 0.1871468  1.0418689635 0.300093154
688        688    D -0.1670978013 0.1874218 -0.8915600180 0.374890006
689        689    D  0.0240597818 0.1881647  0.1278655576 0.898522604
690        690    D  0.0216111114 0.1881677  0.1148502639 0.908820773
691        691    D -0.1638329909 0.1874512 -0.8740032880 0.384548991
692        692    D  0.0343654225 0.1881484  0.1826506682 0.855453336
693        693    D  0.3218829953 0.1853500  1.7366225818 0.085650955
694        694    D -0.1780259877 0.1873191 -0.9503887618 0.344312436
695        695    D -0.0777477036 0.1880164 -0.4135155050 0.680142958
696        696    D  0.3022259931 0.1856874  1.6276064358 0.106831850
697        697    D  0.2626679132 0.1863004  1.4099161978 0.161731801
698        698    D -0.2159894115 0.1869113 -1.1555719686 0.250722796
699        699    D -0.0066777209 0.1881792 -0.0354859733 0.971765791
700        700    D  0.1980109943 0.1871143  1.0582353886 0.292640074
701        701    D -0.2287823788 0.1867559 -1.2250344194 0.223678624
702        702    D -0.1044474183 0.1878844 -0.5559133041 0.579579943
703        703    D -0.2535532753 0.1864292 -1.3600514105 0.177004943
704        704    D  0.1443934296 0.1876142  0.7696293599 0.443389105
705        705    D  0.0804932639 0.1880046  0.4281451217 0.669565597
706        706    D -0.0693585541 0.1880499 -0.3688305771 0.713094448
707        707    D  0.1231294476 0.1877689  0.6557500357 0.513544947
708        708    D -0.2091681764 0.1869904 -1.1186037927 0.266045231
709        709    D  0.2576300275 0.1863721  1.3823419252 0.170052837
710        710    D -0.0738424944 0.1880325 -0.3927113771 0.695494126
711        711    D  0.2452637977 0.1865423  1.3147890985 0.191664805
712        712    D -0.2622030739 0.1863071 -1.4073706165 0.162515093
713        713    D -0.0302426495 0.1881556 -0.1607321456 0.872645214
714        714    D -0.2913958861 0.1858640 -1.5677912832 0.120226759
715        715    D  0.4451730479 0.1827283  2.4362571906 0.016652943
716        716    D  0.0763537761 0.1880222  0.4060890548 0.685565511
717        717    D  0.1180279220 0.1878023  0.6284689827 0.531185964
718        718    D -0.1736215441 0.1873613 -0.9266670465 0.356392652
719        719    D  0.2639806022 0.1862814  1.4171063069 0.159721493
720        720    D -0.2158146540 0.1869133 -1.1546242682 0.251080115
721        721    D -0.0907819793 0.1879568 -0.4829938584 0.630188064
722        722    D -0.0431528379 0.1881299 -0.2293779053 0.819091238
723        723    D  0.0084775841 0.1881784  0.0450507755 0.964167400
724        724    D  0.1762132552 0.1873366  0.9406236971 0.349325213
725        725    D -0.2700158411 0.1861931 -1.4501921364 0.150256806
726        726    D  0.3067810415 0.1856112  1.6528157630 0.101774398
727        727    D  0.1501414382 0.1875682  0.8004631927 0.425380554
728        728    D -0.1435769512 0.1876206 -0.7652513807 0.446050086
729        729    D  0.0210433665 0.1881684  0.1118326457 0.911185834
730        730    D  0.0636323706 0.1880706  0.3383430650 0.735849825
731        731    D -0.0618350024 0.1880767 -0.3287754879 0.743124577
732        732    D -0.2916704323 0.1858596 -1.5693055208 0.119886615
733        733    D -0.2071538001 0.1870133 -1.1076956339 0.270755419
734        734    D  0.1144201295 0.1878251  0.6091844979 0.543817742
735        735    D -0.1347073631 0.1876877 -0.7177206110 0.474778065
736        736    D  0.0881829449 0.1879694  0.4691345167 0.640086732
737        737    D -0.0591207945 0.1880856 -0.3143292142 0.753939227
738        738    D  0.2005962543 0.1870862  1.0722128866 0.286262846
739        739    D -0.1958847388 0.1871372 -1.0467442410 0.297793058
740        740    D  0.0888232151 0.1879663  0.4725484963 0.637587820
741        741    D  0.1245903187 0.1877590  0.6635649423 0.508562976
742        742    D  0.2469688067 0.1865194  1.3240921054 0.188615357
743        743    D  0.1305570818 0.1877177  0.6954970295 0.488457993
744        744    D  0.0495533115 0.1881138  0.2634220065 0.792793758
745        745    D  0.5658195750 0.1792903  3.1558856738 0.002126320
746        746    D  0.0604172887 0.1880814  0.3212295023 0.748735102
747        747    D -0.0276606150 0.1881596 -0.1470061083 0.883434932
748        748    D  0.1606695756 0.1874792  0.8569996210 0.393758906
749        749    D  0.2862500623 0.1859455  1.5394296431 0.127059217
750        750    D -0.1792997514 0.1873067 -0.9572520820 0.340798302
751        751    D -0.1253885217 0.1877536 -0.6678354372 0.505947522
752        752    D  0.0360787678 0.1881451  0.1917603569 0.848355486
753        753    D  0.1049443143 0.1878815  0.5585663944 0.577779612
754        754    D  0.1049260056 0.1878816  0.5584686361 0.577913778
755        755    D -0.2443864089 0.1865541 -1.3100031544 0.193455945
756        756    D  0.2388721529 0.1866269  1.2799447384 0.203606882
757        757    D  0.0154434624 0.1881739  0.0820701578 0.934765477
758        758    D -0.2315454645 0.1867211 -1.2400603427 0.218216982
759        759    D -0.3326955261 0.1851551 -1.7968480064 0.075692589
760        760    D -0.3099657859 0.1855572 -1.6704598930 0.098069450
761        761    D  0.0815143542 0.1880001  0.4335866729 0.665542153
762        762    D  0.2777462361 0.1860771  1.4926407530 0.138817749
763        763    D  0.0437032518 0.1881286  0.2323052182 0.816796165
764        764    D -0.1876932103 0.1872228 -1.0025125707 0.318565661
765        765    D -0.0685641041 0.1880529 -0.3646001370 0.716221447
766        766    D  0.2415438717 0.1865918  1.2945039804 0.198559744
767        767    D  0.0844215720 0.1879870  0.4490818603 0.654495607
768        768    D -0.3983022472 0.1838288 -2.1667020137 0.032987215
769        769    D -0.1334952025 0.1876966 -0.7112287328 0.478647865
770        770    D  0.1004715721 0.1879065  0.5346892125 0.594185310
771        771    D -0.2893758027 0.1858962 -1.5566529691 0.122802987
772        772    D  0.0517650163 0.1881077  0.2751881683 0.783751778
773        773    D  0.3844008077 0.1841305  2.0876536564 0.039423794
774        774    D -0.1638480858 0.1874511 -0.8740844431 0.384216427
775        775    D  0.0922279550 0.1879496  0.4907057400 0.624751539
776        776    D  0.3601473598 0.1846302  1.9506413418 0.053956153
777        777    D  0.1274634262 0.1877394  0.6789382019 0.498777906
778        778    D -0.4115687754 0.1835304 -2.2425104895 0.027181900
779        779    D -0.3891797315 0.1840281 -2.1147844875 0.036985540
780        780    D -0.2130773502 0.1869454 -1.1397840939 0.257367294
781        781    D  0.1371553466 0.1876697  0.7308339109 0.466671256
782        782    D -0.2015476697 0.1870758 -1.0773584123 0.284069591
783        783    D  0.0011783136 0.1881803  0.0062616190 0.995016766
784        784    D  0.0452799956 0.1881248  0.2406912890 0.810310058
785        785    D -0.0118048179 0.1881766 -0.0627326569 0.950107183
786        786    D  0.0351084726 0.1881470  0.1866013343 0.852359656
787        787    D  0.1705511666 0.1873901  0.9101398036 0.365211995
788        788    D -0.1973444602 0.1871215 -1.0546327148 0.294211305
789        789    D  0.0754356844 0.1880260  0.4011980970 0.689150726
790        790    D  0.1471868577 0.1875921  0.7846112092 0.434577884
791        791    D  0.0070848210 0.1881790  0.0376493679 0.970048003
792        792    D  0.3481169835 0.1848655  1.8830820751 0.062696341
793        793    D  0.0790973757 0.1880107  0.4207068393 0.674930632
794        794    D -0.1453954103 0.1876063 -0.7750026214 0.440380712
795        795    D  0.1057684534 0.1878768  0.5629670075 0.574743338
796        796    D -0.3221331120 0.1853456 -1.7380135883 0.085394724
797        797    D  0.3912952006 0.1839823  2.1268089308 0.035947906
798        798    D -0.3121771498 0.1855193 -1.6827204002 0.095652402
799        799    D -0.0727191656 0.1880369 -0.3867280684 0.699804407
800        800    D -0.1437179463 0.1876195 -0.7660073679 0.445515017
801        801    D -0.1179112235 0.1878031 -0.6278450919 0.531566140
802        802    D -0.3831937310 0.1841562 -2.0808079991 0.040067076
803        803    D -0.0521344799 0.1881067 -0.2771538090 0.782250809
804        804    D -0.1655310043 0.1874360 -0.8831334338 0.379327292
805        805    D  0.2533762856 0.1864316  1.3590841434 0.177258469
806        806    D  0.0043543580 0.1881799  0.0231393413 0.981588843
807        807    D  0.2135539833 0.1869398  1.1423675919 0.256113653
808        808    D  0.1540445521 0.1875359  0.8214136728 0.413492038
809        809    D -0.2142671192 0.1869315 -1.1462334376 0.254514041
810        810    D  0.0573770411 0.1880911  0.3050492137 0.760975960
811        811    D  0.1923379852 0.1871747  1.0275854297 0.306675146
812        812    D  0.0184076609 0.1881712  0.0978240134 0.922277485
813        813    D  0.0102172188 0.1881775  0.0542956326 0.956811089
814        814    D -0.1425589438 0.1876286 -0.7597934217 0.449307032
815        815    D  0.0277016573 0.1881596  0.1472242815 0.883258885
816        816    D -0.1044261902 0.1878845 -0.5557999633 0.579623558
817        817    D -0.0805205469 0.1880045 -0.4282905122 0.669426490
818        818    D -0.2124243192 0.1869529 -1.1362448380 0.258634956
819        819    D  0.0733436970 0.1880345  0.3900545256 0.697344079
820        820    D  0.3224477726 0.1853400  1.7397636931 0.085128476
821        821    D  0.0819538118 0.1879982  0.4359287324 0.663858445
822        822    D  0.2491333142 0.1864900  1.3359072355 0.184684908
823        823    D -0.1333974476 0.1876973 -0.7107052340 0.478973358
824        824    D  0.3799082028 0.1842257  2.0621893269 0.041927537
825        825    D  0.0332665048 0.1881504  0.1768080764 0.860029708
826        826    D  0.2943941745 0.1858157  1.5843339414 0.116416137
827        827    D -0.3227366824 0.1853349 -1.7413707142 0.085126211
828        828    D -0.2393503752 0.1866207 -1.2825501565 0.202742828
829        829    D  0.0418251482 0.1881329  0.2223169857 0.824555205
830        830    D -0.1564316581 0.1875157 -0.8342321662 0.406283612
831        831    D  0.1050326556 0.1878810  0.5590380902 0.577529183
832        832    D  0.2345880794 0.1866824  1.2566161442 0.211881523
833        833    D  0.1037279452 0.1878884  0.5520720133 0.582261476
834        834    D -0.0726730238 0.1880371 -0.3864823072 0.699988576
835        835    D -0.1422565155 0.1876309 -0.7581721117 0.450172310
836        836    D  0.0218183643 0.1881675  0.1159518407 0.907942902
837        837    D  0.0120551028 0.1881764  0.0640627655 0.949051464
838        838    D -0.0328979268 0.1881510 -0.1748485073 0.861571198
839        839    D -0.0515187428 0.1881084 -0.2738779485 0.784781405
840        840    D -0.2811699348 0.1860246 -1.5114663558 0.133964898
841        841    D  0.2116802705 0.1869616  1.1322128146 0.260379393
842        842    D  0.0484143184 0.1881168  0.2573630567 0.797446180
843        843    D  0.1244731661 0.1877598  0.6629381908 0.509013291
844        844    D  0.0321255195 0.1881524  0.1707420200 0.864798279
845        845    D  0.1442108423 0.1876157  0.7686502828 0.443955391
846        846    D  0.2945593940 0.1858131  1.5852458929 0.116266833
847        847    D  0.2091312825 0.1869908  1.1184039707 0.266212683
848        848    D -0.1963794510 0.1871319 -1.0494174911 0.296770288
849        849    D  0.1639013625 0.1874506  0.8743708764 0.384176177
850        850    D -0.2847925036 0.1859684 -1.5314029364 0.128900087
851        851    D  0.1591474046 0.1874924  0.8488204943 0.398174007
852        852    D -0.0241301395 0.1881646 -0.1282395359 0.898240127
853        853    D  0.0091453729 0.1881781  0.0485995584 0.961341607
854        854    D  0.1660093583 0.1874317  0.8857059255 0.377981583
855        855    D  0.1442836448 0.1876151  0.7690406648 0.443732907
856        856    D  0.1270561011 0.1877422  0.6767584152 0.500165044
857        857    D  0.0039050900 0.1881800  0.0207518907 0.983488055
858        858    D -0.2020637917 0.1870701 -1.0801501079 0.282772027
859        859    D -0.0717354504 0.1880408 -0.3814887465 0.703715461
860        860    D  0.2811238491 0.1860253  1.5112128421 0.134076080
861        861    D  0.0653756153 0.1880645  0.3476234410 0.728871180
862        862    D  0.0769959322 0.1880196  0.4095101942 0.683063322
863        863    D  0.0695070340 0.1880493  0.3696212537 0.712495382
864        864    D  0.0567884692 0.1880929  0.3019171027 0.763355056
865        865    D -0.1728812261 0.1873683 -0.9226813614 0.358634055
866        866    D  0.2935837753 0.1858288  1.5798614005 0.117489268
867        867    D  0.1045139668 0.1878840  0.5562686214 0.579355652
868        868    D  0.1878551211 0.1872211  1.0033862541 0.318151951
869        869    D -0.0793044552 0.1880098 -0.4218102603 0.674090717
870        870    D  0.0401599960 0.1881366  0.2134618508 0.831413705
871        871    D  0.0148796692 0.1881744  0.0790738344 0.937138019
872        872    D -0.0912485140 0.1879545 -0.4854819505 0.628432707
873        873    D  0.0513630226 0.1881088  0.2730494965 0.785397939
874        874    D  0.0317954846 0.1881530  0.1689874232 0.866174145
875        875    D -0.0929603629 0.1879459 -0.4946122603 0.621980998
876        876    D -0.1577241941 0.1875047 -0.8411746755 0.402417463
877        877    D -0.0305901997 0.1881550 -0.1625797839 0.871185091
878        878    D  0.0908403299 0.1879565  0.4833050447 0.630082532
879        879    D  0.0332521738 0.1881504  0.1767318843 0.860091186
880        880    D  0.1268926775 0.1877433  0.6758838868 0.500719867
881        881    D -0.0016883114 0.1881803 -0.0089717758 0.992859900
882        882    D -0.0168847917 0.1881726 -0.0897303201 0.928685073
883        883    D -0.4946714092 0.1814247 -2.7265937081 0.007620342
884        884    D  0.2944990024 0.1858140  1.5849125485 0.116225673
885        885    D -0.0745133715 0.1880298 -0.3962849475 0.692779633
886        886    D  0.0652084985 0.1880651  0.3467337348 0.729534938
887        887    D -0.0335195900 0.1881499 -0.1781536326 0.858972013
888        888    D -0.0224426940 0.1881667 -0.1192702627 0.905305455
889        889    D -0.1664896678 0.1874273 -0.8882891129 0.376865584
890        890    D  0.5909769532 0.1784602  3.3115337892 0.001316998
891        891    D -0.0218383551 0.1881674 -0.1160580949 0.907845133
892        892    D -0.0211181133 0.1881683 -0.1122299300 0.910884800
893        893    D -0.0316066721 0.1881533 -0.1679836285 0.866943985
894        894    D  0.2360112624 0.1866641  1.2643636750 0.209340725
895        895    D  0.0202067228 0.1881693  0.1073858611 0.914702584
896        896    D  0.0972053478 0.1879240  0.5172587773 0.606196553
897        897    D -0.0338368887 0.1881493 -0.1798406007 0.857649719
898        898    D  0.1368965592 0.1876716  0.7294474650 0.467523701
899        899    D  0.0212196556 0.1881682  0.1127696353 0.910450392
900        900    D  0.0766647707 0.1880210  0.4077458859 0.684352857
901        901    D  0.0085743504 0.1881784  0.0455650131 0.963751260
902        902    D  0.1055290596 0.1878782  0.5616886946 0.575650931
903        903    D  0.1543197076 0.1875336  0.8228910165 0.412812252
904        904    D -0.1390718236 0.1876553 -0.7411027172 0.460411466
905        905    D  0.0587802696 0.1880867  0.3125169262 0.755321062
906        906    D  0.3172105056 0.1854322  1.7106551046 0.090406008
907        907    D -0.3932926331 0.1839388 -2.1381707121 0.035123801
908        908    D -0.1412110497 0.1876390 -0.7525678629 0.453531278
909        909    D  0.2245712383 0.1868080  1.2021498310 0.232246988
910        910    D  0.0626569963 0.1880739  0.3331509309 0.739732056
911        911    D -0.1282632754 0.1877338 -0.6832188553 0.496104913
912        912    D  0.0581146288 0.1880888  0.3089744481 0.758002066
913        913    D -0.2315046154 0.1867216 -1.2398381399 0.218001644
914        914    D -0.1718663078 0.1873778 -0.9172180202 0.361402478
915        915    D  0.4089897339 0.1835892  2.2277441035 0.028317181
916        916    D -0.0872660208 0.1879738 -0.4642456827 0.643501908
917        917    D  0.2633188541 0.1862910  1.4134813805 0.160682909
918        918    D -0.2213909180 0.1868468 -1.1848796242 0.238974394
919        919    D  0.2149945247 0.1869230  1.1501771713 0.252889955
920        920    D -0.1774972003 0.1873242 -0.9475399377 0.345694579
921        921    D  0.0213194877 0.1881681  0.1133002523 0.910030824
922        922    D -0.2016707441 0.1870744 -1.0780240968 0.283836541
923        923    D -0.3463593129 0.1848992 -1.8732329086 0.064035673
924        924    D -0.2317327569 0.1867188 -1.2410791610 0.217600970
925        925    D -0.3075086185 0.1855989 -1.6568453312 0.100861368
926        926    D  0.4630190018 0.1822752  2.5402199170 0.012718515
927        927    D -0.1734273326 0.1873631 -0.9256214180 0.356945244
928        928    D  0.1921122418 0.1871771  1.0263664002 0.307446097
929        929    D  0.3888379663 0.1840355  2.1128427157 0.037277424
930        930    D  0.3953414818 0.1838940  2.1498333519 0.034188487
931        931    D -0.0906533658 0.1879574 -0.4823079613 0.630682670
932        932    D  0.1209587836 0.1877833  0.6441403533 0.521179662
933        933    D  0.1551751232 0.1875264  0.8274841984 0.409976032
934        934    D  0.3775654046 0.1842748  2.0489257938 0.043144113
935        935    D  0.0805858871 0.1880042  0.4286387094 0.669155265
936        936    D -0.0001591084 0.1881804 -0.0008455101 0.999327112
937        937    D  0.0965043981 0.1879277  0.5135187408 0.608748554
938        938    D -0.0519185103 0.1881073 -0.2760047917 0.783128431
939        939    D  0.0312188548 0.1881539  0.1659218682 0.868579376
940        940    D  0.0505260212 0.1881111  0.2685966344 0.788828090
941        941    D  0.1645808080 0.1874445  0.8780239950 0.382146048
942        942    D -0.1675343473 0.1874178 -0.8939082016 0.373563912
943        943    D  0.1803669101 0.1872963  0.9630032216 0.337930051
944        944    D -0.1159649102 0.1878154 -0.6174408490 0.538412148
945        945    D  0.1477183352 0.1875878  0.7874622588 0.432911728
946        946    D -0.0003544457 0.1881804 -0.0018835423 0.998501094
947        947    D  0.2627148548 0.1862997  1.4101732776 0.161837369
948        948    D  0.0131644365 0.1881757  0.0699582257 0.944382045
949        949    D  0.2223357512 0.1868353  1.1900092654 0.236951568
950        950    D -0.0048433990 0.1881797 -0.0257381533 0.979518601
951        951    D  0.0244222058 0.1881642  0.1297919867 0.896998323
952        952    D -0.1962438782 0.1871333 -1.0486848813 0.297168827
953        953    D  0.0597692882 0.1880835  0.3177806126 0.751379819
954        954    D -0.0754276834 0.1880261 -0.4011554747 0.689179248
955        955    D -0.1939764000 0.1871574 -1.0364343668 0.302720215
956        956    D  0.2692785872 0.1862040  1.4461479006 0.151333917
957        957    D  0.0577296755 0.1880900  0.3069258167 0.759563027
958        958    D  0.0368278373 0.1881436  0.1957432376 0.845225931
959        959    D -0.1843197442 0.1872570 -0.9843143272 0.327390066
960        960    D -0.0740925273 0.1880315 -0.3940432130 0.694428504
961        961    D  0.2523700149 0.1864456  1.3535854955 0.178988196
962        962    D -0.0695058196 0.1880493 -0.3696147871 0.712481503
963        963    D  0.2639323589 0.1862821  1.4168420208 0.160020694
964        964    D -0.1295452377 0.1877248 -0.6900804894 0.491824752
965        965    D -0.1163097194 0.1878132 -0.6192839173 0.537220818
966        966    D -0.1194344938 0.1877932 -0.6359893532 0.526266899
967        967    D -0.1818610577 0.1872815 -0.9710571170 0.333974991
968        968    D  0.2699424451 0.1861942  1.4497894882 0.150394826
969        969    D  0.0776819375 0.1880167  0.4131651065 0.680394951
970        970    D  0.1243453088 0.1877607  0.6622541797 0.509385099
971        971    D -0.1700123354 0.1873951 -0.9072401625 0.366577972
972        972    D  0.3378920046 0.1850590  1.8258607013 0.071217264
973        973    D -0.0543077219 0.1881004 -0.2887166822 0.773408882
974        974    D -0.0730340845 0.1880357 -0.3884054122 0.698576817
975        975    D  0.1000386096 0.1879088  0.5323783962 0.595800831
976        976    D  0.0098591257 0.1881777  0.0523926247 0.958331952
977        977    D  0.2722372411 0.1861601  1.4623820239 0.146843089
978        978    D  0.0905166497 0.1879581  0.4815788603 0.631181789
979        979    D  0.0357434323 0.1881457  0.1899773735 0.849751598
980        980    D  0.1145542049 0.1878243  0.6099010368 0.543359456
981        981    D -0.0755271118 0.1880257 -0.4016851460 0.688804464
982        982    D  0.3042643656 0.1856534  1.6388837073 0.104652038
983        983    D  0.3512700620 0.1848047  1.9007640093 0.060348489
984        984    D -0.3619354086 0.1845945 -1.9607047573 0.052760702
985        985    D -0.0643086052 0.1880682 -0.3419429752 0.733129923
986        986    D -0.1248011166 0.1877576 -0.6646927040 0.507869302
987        987    D  0.1221635701 0.1877753  0.6505837605 0.516848331
988        988    D -0.3229263433 0.1853315 -1.7424257492 0.084918592
989        989    D  0.1608528964 0.1874776  0.8579847817 0.393028671
990        990    D  0.3947600648 0.1839068  2.1465228910 0.034445357
991        991    D  0.0949213739 0.1879359  0.5050730497 0.614642742
992        992    D -0.0145640428 0.1881746 -0.0773964230 0.938473668
993        993    D  0.2461230992 0.1865308  1.3194772590 0.190160515
994        994    D -0.2246358607 0.1868072 -1.2025008644 0.232085504
995        995    D  0.0287986601 0.1881579  0.1530558213 0.878676812
996        996    D -0.0843542311 0.1879874 -0.4487229027 0.654628605
997        997    D -0.1017955399 0.1878992 -0.5417560632 0.589288478
998        998    D  0.0079708015 0.1881787  0.0423576288 0.966305745
999        999    D  0.1881300175 0.1872183  1.0048696697 0.317508581
1000      1000    D  0.0571169562 0.1880919  0.3036651493 0.762048710
         conf.low    conf.high       df outcome
1    -0.257401024  0.488083478 97.56246       Y
2    -0.554674724  0.189378531 90.45119       Y
3    -0.073288075  0.664391579 95.27674       Y
4    -0.440055266  0.306389531 97.47826       Y
5    -0.107464262  0.631974126 97.99182       Y
6    -0.210973317  0.533260089 96.37068       Y
7    -0.271537380  0.474989463 90.56870       Y
8    -0.401305227  0.345489818 97.96644       Y
9    -0.493480127  0.252286592 93.41292       Y
10   -0.145718265  0.595690516 97.99895       Y
11   -0.362562959  0.384773547 93.26586       Y
12   -0.693798673  0.041826806 95.16538       Y
13   -0.204739627  0.539893030 90.37705       Y
14   -0.527647679  0.216683328 97.35870       Y
15   -0.594951460  0.146540747 97.52113       Y
16   -0.508850592  0.236512474 93.14713       Y
17   -0.526772479  0.217758439 95.65075       Y
18   -0.152056350  0.589653213 97.96544       Y
19   -0.192007205  0.551895790 92.81085       Y
20   -0.387839713  0.359305154 95.03726       Y
21   -0.375969435  0.371179066 95.21183       Y
22   -0.244783597  0.500449077 96.77883       Y
23   -0.306356704  0.441228084 86.85719       Y
24   -0.332942221  0.413773597 97.83283       Y
25   -0.722333946  0.012761660 81.27898       Y
26   -0.240451711  0.504559949 97.84388       Y
27   -0.204444957  0.539951255 92.48379       Y
28   -0.306919712  0.440241176 90.59252       Y
29   -0.199439220  0.544748328 92.74930       Y
30   -0.452457652  0.293761327 97.77840       Y
31   -0.502188916  0.242974485 96.98437       Y
32   -0.320018098  0.426728071 96.17703       Y
33   -0.411021229  0.335977409 95.20102       Y
34   -0.633869087  0.105488891 97.67129       Y
35   -0.495022521  0.250696371 93.47787       Y
36   -0.313423825  0.433077285 97.88772       Y
37   -0.435283081  0.311349481 96.24445       Y
38   -0.203784596  0.540359218 94.72147       Y
39   -0.401225064  0.345607458 97.58099       Y
40   -0.292844998  0.453471878 96.59542       Y
41   -0.739572029 -0.007211213 91.57912       Y
42   -0.457392280  0.289110153 94.07766       Y
43   -0.061431591  0.676272203 87.82609       Y
44   -0.548735064  0.194921347 96.38157       Y
45   -0.536494857  0.207919598 93.48983       Y
46   -0.435753520  0.311096984 94.04070       Y
47   -0.434606175  0.311875516 97.88083       Y
48   -0.466249781  0.279713933 97.74096       Y
49   -0.427305494  0.319482825 95.68842       Y
50   -0.309760388  0.436878035 95.96795       Y
51   -0.489080676  0.256798365 93.42708       Y
52   -0.248041145  0.497748713 92.13334       Y
53   -0.524301240  0.220868138 90.47374       Y
54   -0.626248642  0.113523185 97.97721       Y
55   -0.652100589  0.087170534 88.16199       Y
56   -0.318685783  0.428298958 93.66225       Y
57   -0.090561513  0.648571460 91.26777       Y
58   -0.349905192  0.396955412 97.53505       Y
59   -0.602504569  0.138713149 96.42495       Y
60   -0.282502880  0.463613731 96.71514       Y
61   -0.863908765 -0.143262510 83.39433       Y
62   -0.602628120  0.138814524 94.17082       Y
63   -0.539005062  0.205120451 95.38574       Y
64   -0.115582966  0.624315454 97.80989       Y
65   -0.131976820  0.608829304 97.23435       Y
66   -0.752303419 -0.021473375 95.50193       Y
67   -0.476990354  0.268721231 97.96073       Y
68   -0.666783229  0.070909563 93.62386       Y
69   -0.429637580  0.316994216 96.98606       Y
70   -0.117412232  0.622844434 95.06809       Y
71   -0.440703168  0.305893287 95.84444       Y
72   -0.539070405  0.204972937 96.17396       Y
73   -0.313693636  0.432974124 96.19657       Y
74   -0.427978528  0.318578638 97.96278       Y
75   -0.166369877  0.575997470 97.79537       Y
76   -0.453324639  0.293080866 95.73258       Y
77   -0.037114244  0.698850753 88.70385       Y
78    0.053519231  0.781520879 96.65965       Y
79   -0.342235823  0.404596731 97.35835       Y
80   -0.206711168  0.537502641 95.06011       Y
81   -0.494378415  0.251209714 94.89505       Y
82    0.019583546  0.750631282 94.83046       Y
83   -0.259294816  0.486346972 96.40401       Y
84   -0.494877997  0.251166078 90.54252       Y
85   -0.494193249  0.251092287 97.98502       Y
86   -0.532298870  0.212253915 93.59699       Y
87   -0.365975565  0.380915374 97.77709       Y
88   -0.142842871  0.598429043 97.98926       Y
89   -0.101062425  0.638045149 97.68481       Y
90   -0.010690459  0.722519553 97.02282       Y
91   -0.448732703  0.297610207 97.14718       Y
92   -0.404535930  0.342235796 97.99489       Y
93   -0.709625961  0.024968332 93.54376       Y
94   -0.298299595  0.448037526 97.32303       Y
95   -0.227363265  0.517626550 94.11685       Y
96   -0.285759184  0.460542805 95.45574       Y
97   -0.165818891  0.576515771 97.88952       Y
98   -0.501753923  0.243354127 97.67687       Y
99   -0.302429814  0.444470957 92.37838       Y
100  -0.454791730  0.291402639 97.61037       Y
101  -0.503753657  0.241486008 95.77150       Y
102  -0.123192062  0.617101708 97.89591       Y
103  -0.070155967  0.667395742 94.57045       Y
104  -0.280005415  0.465941676 97.97823       Y
105  -0.186618375  0.556937021 94.16855       Y
106  -0.714706367  0.019291674 95.42524       Y
107  -0.274433456  0.471432838 97.62932       Y
108  -0.426224487  0.321521485 87.13496       Y
109  -0.645113505  0.093550391 97.81214       Y
110  -0.561008438  0.182123947 96.66136       Y
111  -0.148812503  0.593146089 93.81893       Y
112  -0.533757174  0.212090848 82.42707       Y
113  -0.472788066  0.273318388 94.92637       Y
114  -0.236338982  0.508547163 97.93150       Y
115  -0.321580895  0.425646577 91.68534       Y
116  -0.222211057  0.522424126 96.05871       Y
117  -0.553476619  0.189918503 97.12489       Y
118  -0.300019022  0.446341258 97.36522       Y
119  -0.055962016  0.680976848 91.56523       Y
120  -0.416623986  0.330212998 96.32593       Y
121  -0.342466821  0.404421431 96.79862       Y
122  -0.049819330  0.686202779 96.71792       Y
123  -0.713052106  0.020953286 96.64206       Y
124  -0.471919963  0.274080958 96.15451       Y
125  -0.402944592  0.343956708 96.76388       Y
126  -0.466073939  0.280518390 91.67763       Y
127  -0.212571044  0.531615552 97.43115       Y
128  -0.589257462  0.153730448 86.51538       Y
129  -0.503430602  0.242293601 91.28765       Y
130  -0.104683882  0.634911538 94.70416       Y
131  -0.431711801  0.314809858 97.85599       Y
132  -0.427197168  0.319543238 96.18022       Y
133  -0.289457511  0.457096004 93.64186       Y
134  -0.085240278  0.652985257 97.23883       Y
135  -0.270506067  0.475642879 93.90946       Y
136  -0.173651011  0.569040187 97.65185       Y
137  -0.264397227  0.481667107 93.39566       Y
138  -0.146357952  0.595158481 97.16949       Y
139   0.076785174  0.802690979 96.54811       Y
140  -0.320378040  0.426200477 97.95618       Y
141  -0.514695412  0.230550445 92.57918       Y
142  -0.445669708  0.300719899 97.17312       Y
143  -0.488188888  0.257259572 97.90736       Y
144  -0.460362605  0.286317182 91.89961       Y
145  -0.107199726  0.632358451 96.54741       Y
146  -0.537841532  0.206631300 92.49132       Y
147  -0.465064583  0.280932187 97.64635       Y
148  -0.627300705  0.112464112 97.43031       Y
149  -0.407565158  0.339222443 97.60678       Y
150  -0.430066910  0.316690070 95.67103       Y
151  -0.535941075  0.208079229 97.55892       Y
152  -0.388894514  0.358353630 93.99848       Y
153  -0.161359574  0.580865161 96.97026       Y
154  -0.436115825  0.310730154 94.03698       Y
155  -0.319180106  0.427651597 95.21879       Y
156  -0.220701658  0.523878896 96.12291       Y
157  -0.430110837  0.316434013 97.82274       Y
158  -0.451244687  0.295180064 95.89680       Y
159  -0.061752335  0.674956362 97.80744       Y
160  -0.393528342  0.354250946 88.99958       Y
161  -0.276178876  0.470081660 93.99871       Y
162  -0.464255407  0.281959385 95.60470       Y
163  -0.047265807  0.689360010 89.05240       Y
164  -0.283978236  0.462848147 90.15748       Y
165  -0.364965143  0.381947766 97.52980       Y
166  -0.405056449  0.341962437 95.44109       Y
167  -0.085809945  0.652620687 95.43078       Y
168  -0.649174838  0.089320612 96.94975       Y
169  -0.487017037  0.258469931 97.81291       Y
170  -0.561587108  0.182163009 90.61633       Y
171  -0.645456022  0.094330861 87.34750       Y
172  -0.200379059  0.543327811 97.97913       Y
173  -0.322143385  0.424461651 97.88393       Y
174  -0.299311305  0.447426073 93.47186       Y
175  -0.398035200  0.348960424 96.09832       Y
176  -0.210556526  0.533647463 96.52781       Y
177  -0.383276528  0.363618728 97.68617       Y
178  -0.334602126  0.412216372 96.91076       Y
179  -0.477478012  0.268254314 97.63113       Y
180  -0.230431685  0.514645869 94.17582       Y
181  -0.386338598  0.360560223 97.57108       Y
182  -0.435010365  0.311541235 97.10333       Y
183  -0.601587603  0.139546162 97.75261       Y
184  -0.565877114  0.177282337 94.37028       Y
185  -0.409041814  0.339040338 85.72842       Y
186  -0.590841377  0.150880507 97.24690       Y
187  -0.702822135  0.033290663 85.09257       Y
188  -0.332094572  0.415122154 92.76955       Y
189  -0.224360049  0.520220045 97.34137       Y
190  -0.397854468  0.349004382 97.50500       Y
191  -0.352558788  0.395882218 83.56458       Y
192  -0.400294176  0.346642703 96.56574       Y
193  -0.370528651  0.376462846 96.78931       Y
194  -0.533260256  0.211563786 90.80471       Y
195  -0.721027395  0.012218955 97.88215       Y
196  -0.252434693  0.493262023 94.13226       Y
197  -0.533640013  0.210426111 97.93533       Y
198  -0.489228928  0.256434907 95.46477       Y
199  -0.326742564  0.419900377 97.99179       Y
200  -0.367241485  0.381384928 82.51251       Y
201  -0.434640204  0.311877928 97.49832       Y
202  -0.580525113  0.162037902 93.81811       Y
203  -0.411275340  0.336073682 91.84908       Y
204  -0.309823257  0.436742027 96.72400       Y
205  -0.171694351  0.570994521 96.80218       Y
206  -0.226366978  0.518662766 93.42443       Y
207  -0.456168530  0.290792301 90.07577       Y
208  -0.253010740  0.492322698 97.99949       Y
209  -0.398980326  0.348069201 95.50822       Y
210  -0.334324606  0.412392099 97.94735       Y
211  -0.561772570  0.181239332 97.55874       Y
212  -0.512501299  0.232408353 96.47168       Y
213  -0.526497660  0.217840283 97.68891       Y
214  -0.397620726  0.350043150 89.83666       Y
215  -0.741502833 -0.009485446 93.19903       Y
216  -0.269035387  0.476747166 97.28550       Y
217  -0.445992042  0.300367427 97.43053       Y
218  -0.614392546  0.127807389 82.66221       Y
219  -0.378028357  0.369361684 92.86611       Y
220  -0.142852055  0.598549078 96.61359       Y
221   0.161889810  0.879307132 94.84163       Y
222  -0.187690079  0.555795758 95.28894       Y
223  -0.108047600  0.631424687 97.97437       Y
224  -0.059093659  0.677570914 96.41699       Y
225  -0.399306540  0.347837885 94.55685       Y
226  -0.319206383  0.427356998 97.97431       Y
227  -0.371614342  0.376741336 84.60542       Y
228  -0.257691666  0.487803735 97.52272       Y
229  -0.099199720  0.639774500 97.98211       Y
230  -0.046167606  0.689495481 97.94034       Y
231  -0.190005913  0.553704567 93.93893       Y
232  -0.502724759  0.242422348 96.99519       Y
233  -0.139830929  0.601426831 96.57932       Y
234  -0.194015985  0.549694769 95.47151       Y
235  -0.392582747  0.354807543 92.52241       Y
236  -0.443856035  0.302482025 97.99715       Y
237  -0.552188113  0.191341429 96.28987       Y
238  -0.234637774  0.511116123 89.04386       Y
239  -0.312237513  0.434358197 96.74183       Y
240  -0.542609241  0.201185145 97.35795       Y
241  -0.174769581  0.568549607 91.80659       Y
242  -0.552207384  0.191217432 97.33883       Y
243  -0.361039744  0.385819400 97.99998       Y
244  -0.549939495  0.193566377 97.42698       Y
245  -0.265794850  0.479896034 97.48320       Y
246  -0.424005926  0.323034024 93.60281       Y
247  -0.446805466  0.299555825 97.27880       Y
248  -0.472097913  0.273791623 97.24318       Y
249  -0.494350660  0.250981027 97.46537       Y
250  -0.184611099  0.558685702 95.98412       Y
251  -0.571479380  0.171251034 96.17164       Y
252  -0.494630252  0.250896842 95.42656       Y
253  -0.492181257  0.255036349 81.74920       Y
254  -0.501773368  0.243427507 96.72388       Y
255  -0.506419678  0.239005054 93.24276       Y
256  -0.349835321  0.397121652 96.53715       Y
257  -0.438387498  0.308168812 96.58232       Y
258  -0.144215108  0.597128436 97.92782       Y
259  -0.198966233  0.544699470 97.86710       Y
260  -0.745275078 -0.013992410 97.14885       Y
261  -0.582268989  0.159876128 97.11315       Y
262  -0.376141908  0.371556352 90.06627       Y
263  -0.609859650  0.131101155 95.15390       Y
264  -0.558831916  0.184408442 96.48635       Y
265  -0.421878380  0.324937925 96.00970       Y
266  -0.583220134  0.158810932 97.82186       Y
267  -0.378979591  0.368143976 95.43409       Y
268  -0.410082534  0.337046084 94.00851       Y
269  -0.188546219  0.554714210 97.99468       Y
270  -0.311945321  0.434659041 96.61347       Y
271  -0.208546281  0.535940820 92.99703       Y
272  -0.072593848  0.665677092 89.12609       Y
273  -0.645849906  0.093033229 95.16980       Y
274  -0.227365850  0.517695835 93.41472       Y
275  -0.825815345 -0.101578118 89.41795       Y
276  -0.327590946  0.419655867 92.09143       Y
277  -0.391825560  0.355265779 95.42828       Y
278  -0.455648262  0.290956810 93.40129       Y
279  -0.376133128  0.370792652 97.46871       Y
280  -0.017488325  0.716458826 94.57283       Y
281  -0.340285718  0.406619719 96.46893       Y
282  -0.070538518  0.667229374 92.64844       Y
283  -0.248807954  0.496894679 93.15679       Y
284  -0.486645663  0.258927222 97.02596       Y
285  -0.697657749  0.037433063 97.62654       Y
286  -0.420926771  0.325714458 97.90051       Y
287  -0.374616553  0.372265789 97.92835       Y
288  -0.572278683  0.170499486 95.35117       Y
289  -0.187853736  0.555691879 94.74930       Y
290  -0.342178280  0.405458162 89.66573       Y
291  -0.306210758  0.440457741 95.16677       Y
292  -0.318400950  0.428211889 97.35687       Y
293  -0.537847042  0.206063305 97.97938       Y
294  -0.394973737  0.352087340 95.59507       Y
295  -0.601805806  0.139315329 97.76708       Y
296  -0.243146008  0.502242491 94.73594       Y
297  -0.189975591  0.554396168 87.82921       Y
298  -0.216875218  0.527580502 96.12347       Y
299  -0.380498463  0.366612400 95.54041       Y
300  -0.412144174  0.334574471 97.94887       Y
301  -0.104294044  0.635695939 90.64765       Y
302  -0.347105553  0.399920045 95.69410       Y
303  -0.593174515  0.148370689 97.88166       Y
304  -0.102204223  0.637590850 91.37129       Y
305  -0.162729052  0.580006209 92.43799       Y
306  -0.076326207  0.662164360 89.24355       Y
307  -0.468092419  0.278001696 96.03123       Y
308  -0.719230888  0.014362774 95.84940       Y
309  -0.148696451  0.593024011 96.18440       Y
310  -0.743159081 -0.011766727 97.90215       Y
311  -0.230186580  0.514947916 93.54536       Y
312  -0.240848381  0.504733532 92.23967       Y
313  -0.299328058  0.447000010 97.58896       Y
314  -0.497620575  0.248642901 88.02150       Y
315  -0.591192228  0.150463285 97.74958       Y
316  -0.103526628  0.635867292 96.11521       Y
317  -0.479276348  0.266520222 96.55371       Y
318  -0.268002439  0.477775857 97.08972       Y
319  -0.367700504  0.379180073 97.91126       Y
320  -0.065878775  0.671757513 91.06386       Y
321  -0.002906884  0.729772846 96.36720       Y
322  -0.564569904  0.178310278 97.69446       Y
323  -0.194869542  0.549195998 92.29326       Y
324  -0.110077777  0.629545969 97.54495       Y
325  -0.439912306  0.306488539 97.95545       Y
326  -0.245581968  0.500005753 93.43295       Y
327  -0.162902776  0.579649129 94.30908       Y
328  -0.475021412  0.270741704 97.88529       Y
329  -0.754531260 -0.023958889 96.07976       Y
330  -0.384933933  0.362506880 92.28340       Y
331   0.066051403  0.793118558 94.65587       Y
332  -0.190035651  0.554344365 87.77813       Y
333  -0.317481843  0.429099435 97.57286       Y
334  -0.280412894  0.466895753 85.47090       Y
335  -0.496547872  0.248711424 97.60326       Y
336  -0.121552588  0.619468898 89.80244       Y
337  -0.394789405  0.352992659 88.92813       Y
338  -0.478808803  0.267933264 87.97370       Y
339  -0.393295816  0.355499997 81.03922       Y
340  -0.537809838  0.206157050 97.41174       Y
341  -0.251154281  0.494548474 93.75018       Y
342  -0.276878584  0.469369774 94.25912       Y
343  -0.554808216  0.188458850 97.88690       Y
344  -0.303507063  0.443718957 89.56582       Y
345  -0.378809076  0.368428333 94.31741       Y
346  -0.243626139  0.501572924 96.79945       Y
347  -0.716908662  0.016975055 94.83728       Y
348  -0.178888840  0.564019499 97.64622       Y
349  -0.207220951  0.536861079 96.59420       Y
350  -0.495811442  0.250127068 91.26091       Y
351  -0.009665082  0.723897579 92.55960       Y
352  -0.591635518  0.150279550 94.94577       Y
353  -0.070462869  0.667075637 94.90427       Y
354  -0.639799381  0.099492376 94.80539       Y
355  -0.206015345  0.538219115 94.60694       Y
356  -0.235728921  0.509295059 96.30042       Y
357  -0.545605955  0.198875629 89.82198       Y
358  -0.347697609  0.400287737 86.98248       Y
359  -0.299903831  0.446466123 97.24542       Y
360  -0.095085025  0.643657165 97.93079       Y
361  -0.259910381  0.486020281 93.66338       Y
362  -0.617948933  0.122391516 96.94424       Y
363  -0.229628774  0.515175085 96.70228       Y
364  -0.566140247  0.177142110 93.10280       Y
365  -0.413542889  0.334034712 89.63433       Y
366  -0.547853527  0.195763206 97.12718       Y
367  -0.269378349  0.476424011 97.15761       Y
368  -0.119765152  0.620498119 96.29759       Y
369  -0.518289283  0.226691847 93.99791       Y
370  -0.351687311  0.395387242 95.44185       Y
371  -0.131069599  0.609756249 96.53853       Y
372  -0.670161146  0.066862960 97.94741       Y
373  -0.432980740  0.313759342 95.47433       Y
374  -0.428910800  0.317807066 96.20273       Y
375  -0.058275968  0.678780610 91.89769       Y
376  -0.326565041  0.420494652 93.76784       Y
377  -0.467320716  0.278714140 96.78784       Y
378  -0.615530393  0.124861883 97.77035       Y
379  -0.220919291  0.523669849 96.10665       Y
380  -0.397175188  0.349644131 97.95343       Y
381  -0.628646123  0.111143346 96.39983       Y
382  -0.540495694  0.203332649 97.81952       Y
383  -0.085720664  0.653250958 90.08312       Y
384  -0.309115933  0.438000232 91.27928       Y
385  -0.715050241  0.018724164 97.37752       Y
386  -0.289337822  0.457260313 93.19181       Y
387  -0.699705892  0.035195125 97.99391       Y
388  -0.376401368  0.370475240 97.98015       Y
389  -0.429663729  0.316987015 96.78951       Y
390  -0.452880550  0.294243651 89.15957       Y
391  -0.436661624  0.310657907 89.63967       Y
392  -0.308061634  0.438544320 96.05995       Y
393  -0.463996740  0.282095710 96.88363       Y
394  -0.418610316  0.328521499 93.26078       Y
395  -0.645996064  0.092785638 96.07464       Y
396  -0.212821914  0.531378747 97.37216       Y
397  -0.384210028  0.362764311 96.84801       Y
398  -0.149956694  0.591888199 95.50838       Y
399  -0.270663031  0.475143006 97.41425       Y
400  -0.222333290  0.523159152 88.02958       Y
401  -0.371632532  0.375483399 95.53764       Y
402  -0.581706863  0.160795662 93.87009       Y
403  -0.063529039  0.673848864 92.09329       Y
404  -0.254710101  0.491901203 86.41728       Y
405  -0.512056169  0.233276030 92.53412       Y
406  -0.415039569  0.331664647 97.83664       Y
407  -0.574679459  0.168588853 89.85287       Y
408  -0.411853916  0.335231549 94.28641       Y
409  -0.489789162  0.255966860 94.42765       Y
410  -0.691493445  0.044030649 97.86803       Y
411  -0.587213720  0.154625803 97.83997       Y
412  -0.688418221  0.047775612 93.50631       Y
413  -0.481550023  0.264328199 95.21157       Y
414  -0.370964062  0.376720388 90.18575       Y
415  -0.331143256  0.415812586 95.21503       Y
416  -0.490924628  0.254446556 97.98478       Y
417  -0.280724713  0.465936643 91.07925       Y
418  -0.400780553  0.346017511 97.96762       Y
419  -0.458363044  0.288050087 94.76749       Y
420  -0.127854978  0.612776133 96.86545       Y
421  -0.315716038  0.430911533 96.86868       Y
422   0.026251594  0.756515105 97.38830       Y
423  -0.446556131  0.299985874 95.49759       Y
424  -0.231020338  0.513708543 97.93553       Y
425  -0.610218872  0.130486751 97.50364       Y
426  -0.477347457  0.269304741 89.01601       Y
427  -0.565809297  0.177281905 95.05659       Y
428  -0.167887916  0.575639187 87.31083       Y
429  -0.203653546  0.540170420 97.98929       Y
430  -0.227741602  0.516884196 97.97233       Y
431  -0.218484960  0.525931097 97.08596       Y
432  -0.338928273  0.407957090 96.57337       Y
433  -0.284441214  0.461614700 97.73593       Y
434  -0.284638019  0.462071232 91.33510       Y
435  -0.200947503  0.542975632 95.92418       Y
436  -0.197677052  0.545995523 97.28850       Y
437  -0.682887427  0.053756781 93.01444       Y
438  -0.404465696  0.342375114 97.28224       Y
439  -0.399832500  0.346967977 97.99999       Y
440  -0.305840990  0.440775125 95.63839       Y
441  -0.402183067  0.344759058 96.39766       Y
442  -0.327281857  0.420003859 91.70261       Y
443  -0.386264765  0.360604406 97.88231       Y
444  -0.593799069  0.147727785 97.75267       Y
445  -0.592883623  0.148723240 97.39720       Y
446  -0.493901708  0.251458319 97.29704       Y
447  -0.240144559  0.505531025 91.18039       Y
448  -0.383231792  0.363667740 97.64262       Y
449  -0.475186039  0.270684101 96.75049       Y
450  -0.146831301  0.595667865 87.92936       Y
451   0.000216395  0.733028299 92.51660       Y
452  -0.145278426  0.596322454 95.74431       Y
453  -0.398592370  0.348614779 93.98756       Y
454  -0.616885907  0.123940588 92.81986       Y
455  -0.129298835  0.611320226 97.78559       Y
456  -0.736227286 -0.004149716 96.97248       Y
457  -0.877212773 -0.159794888 97.39962       Y
458  -0.517009930  0.227610432 97.98734       Y
459  -0.233996882  0.511032750 95.72274       Y
460  -0.268218118  0.477792220 94.77590       Y
461  -0.639524512  0.099612990 96.48059       Y
462  -0.211442929  0.532938793 95.01947       Y
463  -0.669529563  0.067709024 96.21564       Y
464  -0.569238555  0.173412635 97.97429       Y
465  -0.328588678  0.418078755 97.92397       Y
466  -0.516481920  0.228859690 91.19811       Y
467  -0.359429777  0.387436769 97.87432       Y
468  -0.148845788  0.593091650 94.04472       Y
469  -0.236113280  0.509477686 90.89549       Y
470  -0.424829334  0.322062728 94.94303       Y
471  -0.313368667  0.433199952 97.17356       Y
472  -0.371728660  0.375357624 95.83464       Y
473  -0.491579739  0.253777403 97.95440       Y
474  -0.479415787  0.267131674 89.50895       Y
475  -0.608292791  0.132951358 93.25002       Y
476  -0.541356221  0.202448016 97.73803       Y
477  -0.388906638  0.357971255 97.70716       Y
478  -0.559152857  0.184151942 95.71411       Y
479  -0.490052572  0.256222193 89.62588       Y
480  -0.484503806  0.261065051 97.60739       Y
481  -0.116984971  0.624107787 87.02645       Y
482  -0.482627473  0.262978368 97.69375       Y
483  -0.516282434  0.228361772 97.97884       Y
484  -0.438151322  0.308313900 97.54826       Y
485  -0.108629701  0.630976547 96.87752       Y
486  -0.323708091  0.423116240 95.79792       Y
487  -0.495860303  0.249706894 94.71344       Y
488  -0.245225494  0.500016818 96.80342       Y
489   0.098896709  0.822577299 97.91145       Y
490  -0.486181141  0.259310955 97.97513       Y
491   0.071381537  0.797789829 96.50927       Y
492  -0.403963967  0.343230698 93.79914       Y
493  -0.398686773  0.348266423 96.49172       Y
494  -0.421144375  0.325601467 96.79904       Y
495  -0.442895092  0.303458042 97.99263       Y
496  -0.438825660  0.307598818 97.87176       Y
497  -0.179094556  0.564268981 93.09273       Y
498  -0.788864163 -0.061076728 91.88487       Y
499  -0.392749898  0.354135088 97.48371       Y
500  -0.432337422  0.314416994 95.41432       Y
501  -0.420891414  0.325746348 97.94046       Y
502  -0.193062833  0.550709549 94.48579       Y
503  -0.104115385  0.635275325 96.49761       Y
504   0.001413902  0.734126378 92.58181       Y
505  -0.160809606  0.581368095 97.20958       Y
506  -0.525054469  0.220264556 88.95930       Y
507  -0.341498375  0.405269552 97.98238       Y
508   0.006550648  0.738683856 94.38268       Y
509  -0.334333099  0.412509482 96.64011       Y
510  -0.109761218  0.630174029 94.11927       Y
511  -0.183386978  0.560584487 89.06136       Y
512  -0.449908850  0.296941417 92.04081       Y
513  -0.382555717  0.364894708 92.24188       Y
514  -0.333470292  0.413766196 92.69679       Y
515  -0.505351769  0.240206761 92.28992       Y
516  -0.690818950  0.044818999 97.21163       Y
517  -0.014056285  0.719782394 93.08867       Y
518  -0.131687926  0.609177948 96.44637       Y
519  -0.501945833  0.243230755 96.92040       Y
520  -0.237102872  0.507984010 96.06264       Y
521  -0.355728371  0.391127056 97.85871       Y
522  -0.558859229  0.184326274 97.02759       Y
523  -0.312819186  0.433767672 96.91120       Y
524  -0.401223211  0.345612499 97.54802       Y
525  -0.363776048  0.383825369 90.83906       Y
526  -0.450910630  0.296991258 83.19145       Y
527  -0.488717853  0.256717386 97.90584       Y
528  -0.779977047 -0.051920372 97.60737       Y
529  -0.274212928  0.472073083 93.35332       Y
530  -0.088534599  0.649839706 97.75523       Y
531  -0.700013629  0.035552228 91.40211       Y
532  -0.167010143  0.576236084 89.43686       Y
533  -0.502538558  0.242597073 97.16596       Y
534  -0.075872453  0.662347301 91.50280       Y
535  -0.485469940  0.260232829 96.01039       Y
536  -0.180140517  0.563503467 90.84021       Y
537  -0.318590079  0.428253305 95.03407       Y
538  -0.334315309  0.412397647 97.98604       Y
539  -0.367498534  0.379540637 96.27379       Y
540  -0.624446485  0.115624048 96.00132       Y
541  -0.209327618  0.536264913 83.65467       Y
542  -0.544248425  0.199471877 97.48221       Y
543  -0.294387277  0.451822355 97.98892       Y
544  -0.406436629  0.340557938 95.58714       Y
545  -0.026739198  0.708232242 91.09567       Y
546  -0.130371033  0.610661293 94.05597       Y
547  -0.546901227  0.197025306 94.43193       Y
548  -0.480715263  0.265453442 92.62984       Y
549   0.074783125  0.800914891 96.10618       Y
550  -0.917860255 -0.205410274 94.53916       Y
551  -0.108847371  0.630674896 97.91110       Y
552  -0.142532445  0.598744506 97.77288       Y
553  -0.256301505  0.489420351 94.84933       Y
554  -0.597506003  0.144054726 95.55422       Y
555  -0.371792549  0.375392191 94.85697       Y
556  -0.055700289  0.680617254 97.75986       Y
557  -0.700271376  0.034983504 94.08202       Y
558  -0.295537869  0.451110094 93.74383       Y
559  -0.590675852  0.150997204 97.82863       Y
560  -0.488611396  0.256822713 97.94552       Y
561  -0.338188649  0.409296835 90.75436       Y
562  -0.517624978  0.227055147 97.17228       Y
563  -0.268110886  0.477647115 97.32737       Y
564  -0.340146364  0.406803442 96.00815       Y
565  -0.420855965  0.325988988 95.82928       Y
566  -0.455202860  0.291373863 93.74564       Y
567  -0.224812071  0.519874350 96.37868       Y
568  -0.532496320  0.212073054 93.37541       Y
569  -0.362669373  0.384646727 93.46272       Y
570  -0.657591222  0.080349636 97.11988       Y
571  -0.261801662  0.483749597 97.97909       Y
572  -0.432177510  0.314838094 92.91993       Y
573  -0.563895121  0.179097056 96.84703       Y
574  -0.470064680  0.276415835 91.94544       Y
575  -0.125301507  0.616323792 86.23788       Y
576  -0.507294118  0.237677491 97.43387       Y
577  -0.108821607  0.632638736 80.58184       Y
578  -0.448213207  0.298113361 97.40217       Y
579  -0.629545125  0.110200849 96.31392       Y
580  -0.844186350 -0.122900246 97.89843       Y
581  -0.662797118  0.075336128 92.01402       Y
582  -0.271610085  0.474485719 94.66799       Y
583  -0.372141475  0.375022852 95.05926       Y
584  -0.154424177  0.588140298 90.52277       Y
585  -0.377881817  0.369010804 97.80015       Y
586  -0.549655320  0.194933073 87.59458       Y
587  -0.264900417  0.480737608 97.82509       Y
588  -0.375645762  0.371234030 97.95117       Y
589  -0.465404367  0.280556566 97.94703       Y
590  -0.301894885  0.444441130 97.92455       Y
591  -0.225669598  0.519133510 95.45815       Y
592  -0.396902847  0.350003646 97.06415       Y
593   0.010568408  0.742123265 97.15931       Y
594  -0.273922318  0.471905395 97.92351       Y
595  -0.292144119  0.454026467 97.99740       Y
596  -0.328932284  0.417743645 97.86907       Y
597  -0.056352902  0.680119021 96.55481       Y
598  -0.560600648  0.183501482 87.95688       Y
599  -0.057253823  0.679614729 93.08170       Y
600  -0.311704283  0.435536873 90.46266       Y
601  -0.156825608  0.585479707 94.05437       Y
602  -0.602018252  0.139577455 93.02782       Y
603  -0.664376931  0.073171675 96.57773       Y
604  -0.484683808  0.261053049 95.86280       Y
605  -0.291721785  0.454936725 93.01780       Y
606  -0.271041818  0.474789095 97.23989       Y
607  -0.191943015  0.552139445 91.09160       Y
608  -0.296091277  0.450271947 96.68023       Y
609  -0.396312228  0.350608783 96.94547       Y
610  -0.684092017  0.052093226 96.60105       Y
611  -0.408033653  0.339604485 89.49098       Y
612  -0.386259435  0.361687169 87.78976       Y
613  -0.398012604  0.348983038 96.09934       Y
614  -0.017547213  0.716582697 92.76620       Y
615  -0.348438975  0.398439829 97.26642       Y
616  -0.561509276  0.181575519 96.92954       Y
617  -0.405412240  0.341412501 97.38157       Y
618  -0.382804109  0.364403131 94.55072       Y
619  -0.298653648  0.447686629 97.34910       Y
620  -0.349668092  0.397193144 97.51591       Y
621   0.063220018  0.791167410 88.51645       Y
622  -0.228901927  0.515889008 96.60668       Y
623  -0.702421121  0.032909662 91.87445       Y
624  -0.432437669  0.314081377 97.78696       Y
625  -0.435276862  0.312163629 88.75807       Y
626  -0.056543262  0.679844618 97.59795       Y
627  -0.322123657  0.424908308 93.58404       Y
628  -0.213914323  0.530525577 95.27768       Y
629  -0.277336812  0.468866547 94.79607       Y
630  -0.480733277  0.265291689 93.97837       Y
631   0.030218355  0.760577054 92.90860       Y
632  -0.134792315  0.606084724 97.99112       Y
633  -0.184356936  0.559114898 94.11104       Y
634  -0.851070031 -0.129786310 90.43077       Y
635  -0.481679284  0.264492763 92.38853       Y
636  -0.096675567  0.642558765 93.75209       Y
637  -0.508890890  0.236350470 94.28881       Y
638  -0.282541473  0.463514423 97.35450       Y
639  -0.313948446  0.432551622 97.96929       Y
640  -0.202485521  0.541343510 97.48835       Y
641  -0.547165934  0.196395487 97.96691       Y
642  -0.612719540  0.127803849 97.99413       Y
643  -0.010998170  0.722331894 95.97866       Y
644  -0.089708004  0.649016493 94.79247       Y
645  -0.571781480  0.171406930 91.70459       Y
646  -0.355129220  0.391788375 97.18705       Y
647  -0.578141302  0.164130772 97.76969       Y
648  -0.439248533  0.307861188 91.17834       Y
649  -0.596036484  0.145477554 96.75067       Y
650  -0.500341767  0.244946269 96.25195       Y
651  -0.260463841  0.485311316 95.33259       Y
652  -0.580261308  0.162267357 94.26055       Y
653  -0.280515953  0.465536835 96.97434       Y
654  -0.490948759  0.254800452 94.20698       Y
655  -0.518450811  0.226520916 94.03824       Y
656  -0.431204720  0.316142981 90.01750       Y
657  -0.564871392  0.177990974 97.74519       Y
658  -0.550098055  0.193660635 94.85002       Y
659  -0.227219673  0.517647676 95.29477       Y
660  -0.328905663  0.418873667 87.50032       Y
661  -0.475446779  0.271248416 89.01390       Y
662  -0.315753614  0.430949027 96.10466       Y
663  -0.323379798  0.423330678 96.92388       Y
664  -0.208816708  0.535194217 97.93220       Y
665  -0.439372390  0.307044816 97.86612       Y
666  -0.589252163  0.152596897 96.74304       Y
667  -0.614946216  0.126431761 88.88494       Y
668  -0.178529088  0.564625316 94.93524       Y
669  -0.590870752  0.150882635 96.91340       Y
670  -0.341117004  0.405771438 96.70257       Y
671  -0.347130063  0.399671351 97.99977       Y
672  -0.327649421  0.419158678 96.37129       Y
673  -0.359640196  0.387840922 91.83777       Y
674  -0.266490413  0.479207054 97.58048       Y
675  -0.441131719  0.305811476 92.45111       Y
676  -0.543777565  0.200980695 88.06094       Y
677  -0.572867202  0.169621125 97.99993       Y
678  -0.066609319  0.670954181 92.21025       Y
679  -0.473789990  0.272298887 94.88431       Y
680  -0.385089102  0.361800170 97.70482       Y
681  -0.259659678  0.486075863 95.53724       Y
682  -0.110724661  0.628892997 97.99582       Y
683  -0.532559092  0.212629803 87.88535       Y
684  -0.346805418  0.401158793 87.11505       Y
685  -0.105094533  0.634955846 90.50376       Y
686  -0.347507851  0.400229354 89.07536       Y
687  -0.176508277  0.566473099 95.85270       Y
688  -0.539195537  0.204999934 94.63758       Y
689  -0.349439964  0.397559527 96.08451       Y
690  -0.352239191  0.395461414 89.60768       Y
691  -0.536470206  0.208804224 86.05659       Y
692  -0.339057061  0.407787906 96.99827       Y
693  -0.046018290  0.689784281 96.31913       Y
694  -0.549873676  0.193821700 95.55357       Y
695  -0.450914442  0.295419035 96.87263       Y
696  -0.066282511  0.670734497 97.62020       Y
697  -0.107041337  0.632377163 97.95287       Y
698  -0.587002912  0.155024089 96.04902       Y
699  -0.380202490  0.366847048 96.15985       Y
700  -0.173473176  0.569495165 94.69800       Y
701  -0.599678497  0.142113740 92.32087       Y
702  -0.477455649  0.268560812 94.79104       Y
703  -0.623621074  0.116514523 95.82162       Y
704  -0.227966757  0.516753616 97.04440       Y
705  -0.292997191  0.453983719 90.24032       Y
706  -0.442800748  0.304083639 92.76710       Y
707  -0.249562911  0.495821806 96.52594       Y
708  -0.580247240  0.161910887 97.94318       Y
709  -0.112283928  0.627543984 96.65156       Y
710  -0.447582420  0.299897431 86.91737       Y
711  -0.124946797  0.615474393 97.50587       Y
712  -0.631972745  0.107566597 96.96386       Y
713  -0.403772245  0.343286946 95.12738       Y
714  -0.660342196  0.077550424 95.81119       Y
715   0.082536369  0.807809727 97.60408       Y
716  -0.296786027  0.449493579 97.66962       Y
717  -0.254746437  0.490802282 96.20758       Y
718  -0.545468136  0.198225047 97.28440       Y
719  -0.105832503  0.633793707 95.04600       Y
720  -0.586784496  0.155155188 97.02809       Y
721  -0.463822546  0.282258587 97.03398       Y
722  -0.416862160  0.330556484 90.77598       Y
723  -0.365410299  0.382365467 89.32324       Y
724  -0.195781274  0.548207784 93.35900       Y
725  -0.639595387  0.099563705 96.22306       Y
726  -0.061854729  0.675416812 92.07504       Y
727  -0.222085919  0.522368795 97.90796       Y
728  -0.516130337  0.228976434 93.45712       Y
729  -0.352390931  0.394477664 97.57575       Y
730  -0.309725482  0.436990223 95.18621       Y
731  -0.435718558  0.312048553 86.00823       Y
732  -0.660626691  0.077285826 95.43353       Y
733  -0.578362771  0.164055171 96.19223       Y
734  -0.258332196  0.487172455 97.59028       Y
735  -0.507553454  0.238138727 90.50556       Y
736  -0.285155710  0.461521600 91.72058       Y
737  -0.432370707  0.314129118 97.99605       Y
738  -0.170679291  0.571871799 97.80960       Y
739  -0.567253505  0.175484027 97.97524       Y
740  -0.284197922  0.461844352 97.83136       Y
741  -0.248119748  0.497300386 95.77224       Y
742  -0.123267502  0.617205115 96.03429       Y
743  -0.242155800  0.503269963 94.09591       Y
744  -0.323882117  0.422988740 95.34956       Y
745   0.210020711  0.921618439 97.93018       Y
746  -0.312923477  0.433758055 95.95623       Y
747  -0.401145948  0.345824718 96.17314       Y
748  -0.211874507  0.533213658 88.53484       Y
749  -0.082949353  0.655449478 93.99600       Y
750  -0.551009202  0.192409699 97.88722       Y
751  -0.498393549  0.247616506 90.00552       Y
752  -0.337628470  0.409786006 91.36023       Y
753  -0.268076066  0.477964695 94.44320       Y
754  -0.268343118  0.478195129 89.83317       Y
755  -0.614898291  0.126125473 92.01094       Y
756  -0.131514682  0.609258988 97.33197       Y
757  -0.358181646  0.389068571 93.97297       Y
758  -0.602563294  0.139472365 88.87956       Y
759  -0.700505988  0.035114936 90.58589       Y
760  -0.678270272  0.058338700 96.48354       Y
761  -0.291568711  0.454597419 97.93888       Y
762  -0.091624353  0.647116825 95.78664       Y
763  -0.329735693  0.417142196 95.86611       Y
764  -0.559231920  0.183845499 97.97560       Y
765  -0.441903358  0.304775150 94.86025       Y
766  -0.128781871  0.611869614 97.15365       Y
767  -0.289252861  0.458096005 86.51030       Y
768  -0.763674207 -0.032930287 87.13023       Y
769  -0.506016890  0.239026485 97.08403       Y
770  -0.272845247  0.473788391 89.86249       Y
771  -0.658318557  0.079566952 97.20144       Y
772  -0.321534590  0.425064623 97.87461       Y
773   0.018998386  0.749803229 97.97113       Y
774  -0.535854337  0.208158166 97.67115       Y
775  -0.280836950  0.465292860 96.24526       Y
776  -0.006245340  0.726540059 97.99964       Y
777  -0.245100962  0.500027815 97.96358       Y
778  -0.775778957 -0.047358594 97.99700       Y
779  -0.754378123 -0.023981340 97.98598       Y
780  -0.584421065  0.158266364 91.00513       Y
781  -0.235394552  0.509705245 95.42636       Y
782  -0.572977470  0.169882130 94.26386       Y
783  -0.372279269  0.374635896 97.58550       Y
784  -0.328166987  0.418726978 95.55395       Y
785  -0.385235827  0.361626191 97.98580       Y
786  -0.338271435  0.408488380 97.82388       Y
787  -0.201799131  0.542901464 88.82326       Y
788  -0.568725505  0.174036585 97.06920       Y
789  -0.297711843  0.448583212 97.66504       Y
790  -0.225092880  0.519466595 97.80373       Y
791  -0.366604919  0.380774561 92.93373       Y
792  -0.018806695  0.715040662 96.65051       Y
793  -0.294208252  0.452403003 93.88367       Y
794  -0.518136043  0.227345223 89.50856       Y
795  -0.267067971  0.478604878 97.97935       Y
796  -0.690011576  0.045745352 96.60861       Y
797   0.026186847  0.756403554 97.96855       Y
798  -0.680391586  0.056037287 96.79322       Y
799  -0.445919241  0.300480910 97.02501       Y
800  -0.516047842  0.228611950 97.89409       Y
801  -0.490601537  0.254779090 97.97325       Y
802  -0.748658764 -0.017728698 97.72162       Y
803  -0.425466330  0.321197370 97.16110       Y
804  -0.537495621  0.206433613 97.91656       Y
805  -0.116619495  0.623372066 97.40477       Y
806  -0.369347722  0.378056438 92.73320       Y
807  -0.157470529  0.584578496 96.98484       Y
808  -0.218319124  0.526408229 93.86945       Y
809  -0.585267156  0.156732918 97.14963       Y
810  -0.315886216  0.430640299 97.94546       Y
811  -0.179105261  0.563781232 97.97543       Y
812  -0.355144075  0.391959397 95.30273       Y
813  -0.363254146  0.383688584 97.18487       Y
814  -0.515170505  0.230052618 92.65224       Y
815  -0.345716952  0.401120266 97.53879       Y
816  -0.477310905  0.268458525 97.28882       Y
817  -0.453843216  0.292802122 93.32290       Y
818  -0.583442973  0.158594335 97.65005       Y
819  -0.299812179  0.446499573 97.84088       Y
820  -0.045482975  0.690378520 95.31411       Y
821  -0.291177287  0.455084911 96.86153       Y
822  -0.120966869  0.619233497 97.64355       Y
823  -0.505927578  0.239132683 96.93893       Y
824   0.014161037  0.745655369 94.73938       Y
825  -0.340184437  0.406717447 96.49784       Y
826  -0.074460837  0.663249186 95.72153       Y
827  -0.691069818  0.045596454 87.67441       Y
828  -0.609797039  0.131096289 95.84687       Y
829  -0.331775389  0.415425685 92.89053       Y
830  -0.528790893  0.215927576 93.18711       Y
831  -0.268244244  0.478309556 89.67503       Y
832  -0.135879830  0.605055989 97.94030       Y
833  -0.269523289  0.476979180 90.38983       Y
834  -0.445889057  0.300543010 96.70491       Y
835  -0.514616565  0.230103534 97.73465       Y
836  -0.351887968  0.395524697 92.19444       Y
837  -0.361400769  0.385510975 97.46004       Y
838  -0.406430395  0.340634541 94.89272       Y
839  -0.425029177  0.321991691 93.67689       Y
840  -0.650440729  0.088100859 95.69808       Y
841  -0.159459610  0.582820151 95.51354       Y
842  -0.324967086  0.421795723 96.55768       Y
843  -0.248390754  0.497337086 92.80929       Y
844  -0.341517631  0.405768670 92.81549       Y
845  -0.228121551  0.516543235 97.68114       Y
846  -0.074373624  0.663492412 94.06205       Y
847  -0.162089147  0.580351712 95.06544       Y
848  -0.568103332  0.175344430 90.82911       Y
849  -0.208354714  0.536157439 92.69211       Y
850  -0.653852782  0.084267775 97.74346       Y
851  -0.213205208  0.531500017 92.43800       Y
852  -0.397855521  0.349595242 91.73714       Y
853  -0.364490129  0.382780875 93.93332       Y
854  -0.206023148  0.538041865 96.33391       Y
855  -0.228068316  0.516635605 97.24998       Y
856  -0.245545828  0.499658030 97.29633       Y
857  -0.369785331  0.377595511 92.95638       Y
858  -0.573378308  0.169250725 96.33957       Y
859  -0.445173493  0.301702592 92.50615       Y
860  -0.088215494  0.650463192 94.35834       Y
861  -0.307848953  0.438600184 97.64905       Y
862  -0.296145446  0.450137311 97.52627       Y
863  -0.303865107  0.442879175 94.08191       Y
864  -0.316475916  0.430052854 97.99772       Y
865  -0.545108225  0.199345773 90.22786       Y
866  -0.075371322  0.662538873 94.24246       Y
867  -0.268558469  0.477586403 93.53127       Y
868  -0.183691062  0.559401304 97.74913       Y
869  -0.452420657  0.293811747 97.64597       Y
870  -0.333227993  0.413547985 97.23028       Y
871  -0.358629857  0.388389196 96.27571       Y
872  -0.464300926  0.281803898 96.69683       Y
873  -0.321999552  0.424725598 96.61867       Y
874  -0.341847118  0.405438087 92.84717       Y
875  -0.465933550  0.280012825 97.98739       Y
876  -0.530093449  0.214645061 92.58292       Y
877  -0.403991927  0.342811527 97.70173       Y
878  -0.282696904  0.464377564 87.77804       Y
879  -0.340221790  0.406726138 96.03259       Y
880  -0.245717721  0.499503076 97.16726       Y
881  -0.375127767  0.371751144 97.96268       Y
882  -0.390317998  0.356548415 97.77552       Y
883  -0.854842308 -0.134500510 95.05407       Y
884  -0.074268310  0.663266315 97.46291       Y
885  -0.447778536  0.298751793 95.41908       Y
886  -0.308001465  0.438418462 97.97932       Y
887  -0.406921614  0.339882434 97.48510       Y
888  -0.395854532  0.350969144 97.97674       Y
889  -0.539088443  0.206109107 85.91030       Y
890   0.236645548  0.945308358 94.11181       Y
891  -0.395272982  0.351596272 97.53073       Y
892  -0.394820054  0.352583827 92.30612       Y
893  -0.405012931  0.341799587 97.53644       Y
894  -0.134793206  0.606815731 90.65095       Y
895  -0.353212863  0.393626309 97.92185       Y
896  -0.275946152  0.470356848 93.53936       Y
897  -0.407221589  0.339547811 97.82232       Y
898  -0.235681322  0.509474440 94.94693       Y
899  -0.352326107  0.394765418 95.30225       Y
900  -0.296473592  0.449803133 97.64621       Y
901  -0.364939407  0.382088108 96.35128       Y
902  -0.267456495  0.478514614 94.99656       Y
903  -0.218405884  0.527045299 87.29447       Y
904  -0.511489021  0.233345374 97.55067       Y
905  -0.314537293  0.432097832 96.63970       Y
906  -0.050915216  0.685336227 95.07409       Y
907  -0.758557746 -0.028027521 93.01861       Y
908  -0.513620305  0.231198206 97.04406       Y
909  -0.146215003  0.595357480 96.50500       Y
910  -0.310569595  0.435883587 97.99898       Y
911  -0.500885135  0.244358584 96.54406       Y
912  -0.315178455  0.431407713 97.22873       Y
913  -0.602056659  0.139047429 97.80952       Y
914  -0.543964753  0.200232138 92.93855       Y
915   0.044402083  0.773577385 92.69315       Y
916  -0.460296214  0.285764172 97.95119       Y
917  -0.106369676  0.633007385 97.99762       Y
918  -0.592253412  0.149471576 96.51782       Y
919  -0.155981387  0.585970436 97.29962       Y
920  -0.549236484  0.194242083 97.99109       Y
921  -0.352225584  0.394864559 95.31142       Y
922  -0.573208034  0.169866545 92.16155       Y
923  -0.713315391  0.020596765 97.37191       Y
924  -0.602367015  0.138901502 95.99072       Y
925  -0.675985417  0.060968180 94.67214       Y
926   0.101105177  0.824932826 93.95592       Y
927  -0.545302197  0.198447532 96.77535       Y
928  -0.179704266  0.563928749 90.77749       Y
929   0.023407628  0.754268304 93.53602       Y
930   0.030117793  0.760565171 92.10777       Y
931  -0.463735489  0.282428757 96.21077       Y
932  -0.252282686  0.494200253 86.96891       Y
933  -0.216971624  0.527321870 97.85836       Y
934   0.011874818  0.743255992 97.93078       Y
935  -0.292643409  0.453815183 95.12399       Y
936  -0.373632480  0.373314264 97.25943       Y
937  -0.276449076  0.469457872 97.64263       Y
938  -0.425234222  0.321397202 97.52055       Y
939  -0.342428041  0.404865750 92.80321       Y
940  -0.322967972  0.424020014 94.09857       Y
941  -0.207543939  0.536705555 94.99453       Y
942  -0.539465012  0.204396317 97.87254       Y
943  -0.191343804  0.552077625 97.42614       Y
944  -0.488796227  0.256866406 95.58493       Y
945  -0.224543618  0.519980288 97.99974       Y
946  -0.373930705  0.373221814 95.17804       Y
947  -0.107258494  0.632688204 92.63764       Y
948  -0.360676962  0.387005835 90.04292       Y
949  -0.148487691  0.593159193 96.85382       Y
950  -0.378286357  0.368599559 97.86603       Y
951  -0.349006195  0.397850606 97.52645       Y
952  -0.568085003  0.175597246 88.80564       Y
953  -0.313838267  0.433376843 90.94944       Y
954  -0.448560560  0.297705193 97.97312       Y
955  -0.565694797  0.177741997 91.85957       Y
956  -0.100248169  0.638805344 97.76944       Y
957  -0.315614693  0.431074044 96.22866       Y
958  -0.336646505  0.410302179 95.75392       Y
959  -0.555935072  0.187295583 97.79129       Y
960  -0.447361815  0.299176760 95.40408       Y
961  -0.117633799  0.622373829 97.81694       Y
962  -0.442768457  0.303756818 96.24989       Y
963  -0.106207194  0.634071911 88.98404       Y
964  -0.502222587  0.243132112 95.07008       Y
965  -0.489195842  0.256576403 94.41699       Y
966  -0.492107279  0.253238292 97.93197       Y
967  -0.553640889  0.189918774 95.41794       Y
968  -0.099676930  0.639561820 95.45889       Y
969  -0.295465552  0.450829427 97.28082       Y
970  -0.248326815  0.497017432 96.60778       Y
971  -0.542044064  0.202019393 94.89174       Y
972  -0.029805066  0.705589075 89.19848       Y
973  -0.427593493  0.318978049 97.86031       Y
974  -0.446286173  0.300218004 95.91606       Y
975  -0.273372100  0.473449319 88.31621       Y
976  -0.363988178  0.383706429 90.01099       Y
977  -0.097201562  0.641676044 97.78684       Y
978  -0.282493111  0.463526411 97.72707       Y
979  -0.338004025  0.409490890 90.65664       Y
980  -0.258244602  0.487353012 96.59656       Y
981  -0.448733048  0.297678825 96.44619       Y
982  -0.064457993  0.672986724 92.02546       Y
983  -0.015588673  0.718128797 95.50293       Y
984  -0.728270706  0.004399889 97.71351       Y
985  -0.437548870  0.308931660 97.47735       Y
986  -0.497582821  0.247980587 94.29962       Y
987  -0.250503270  0.494830410 97.31388       Y
988  -0.691220599  0.045367913 88.22544       Y
989  -0.211266576  0.532972369 96.41722       Y
990   0.029536166  0.759983964 92.58593       Y
991  -0.278036530  0.467879278 97.89154       Y
992  -0.388218149  0.359090063 93.44413       Y
993  -0.124156667  0.616402865 95.61295       Y
994  -0.595378556  0.146106834 97.37339       Y
995  -0.344711190  0.402308510 95.61100       Y
996  -0.457439189  0.288730727 97.36995       Y
997  -0.474950097  0.271359017 92.54924       Y
998  -0.365787031  0.381728634 91.65427       Y
999  -0.183538396  0.559798431 95.13806       Y
1000 -0.316304512  0.430538425 94.76730       Y

Code relies on tidyverse, infer and estimatr packages

Visualize

Visualize

Visualize

Visualize

mean(abs(null_df$estimate) >= abs(obs))

[1] 0.2

Normal-approximation inference

mean(abs(null_df$estimate) >= abs(obs)) # randomization inference p-value

[1] 0.2

Compare with:

difference_in_means(Y ~ D, data = experiment) %>% tidy()  %>% .$p.value

[1] 0.1908766

• Normal approximation compares test statistic to t-distribution

• Based on “weak” null hypothesis \(H_0: E[\tau_i] = 0\)

• vs. randomization inference sharp null \(H_0 : \tau_i = Y_i(1) - Y_i(0) = 0 \forall i\)

Using control variables?

Difference in means gives you an unbiased estimate of the average treatment effect in experiments

But no guarantee for statistical precision

Can use covariates and regression to make standard errors smaller

…and you should! Experiments are expensive

See Bowers (2011) for an extensive discussion

Example

Manekin, Devorah and Tamar Mitts. 2022. “Effective for Whom? Ethnic Identity and Nonviolent Resistance.” American Political Science Review 116(1): 161-180

Data from US Wave 2

• Data
• Output

# Load data from course github
load(url("http://gustavodiaz.org/ps403/data/Manekin_Mitts.rdata"))

# Clean up
w2 = us_survey_wave2 %>% 
  # Redo factors so that they don't have too many levels
  mutate(
    white = ifelse(race == "White / Caucasian", 1, 0)
  ) %>% 
  select(Y = police_action_required, # outcome 11 pt scale
         Z = black, # treatment: race of protesters
         # covariates
         pol_views, white, female, partyID
  ) %>% 
  drop_na # drop incomplete cases, if any

       Y Z pol_views white female partyID
1      9 1         3     1      1       R
2      5 1         2     1      1       D
3      1 0         5     1      1       R
4     10 0         3     1      0       R
5      6 0         3     1      1       I
6      1 0         4     1      0       I
7      6 1         3     1      1       I
8      4 0         5     1      1       R
9      5 1         5     1      1       R
10     5 0         3     1      1       D
11     5 1         1     1      1       I
12     0 0         1     1      1       D
13     0 1         0     0      0       D
14     7 1         5     1      1       R
15     4 1         5     1      0       I
16     3 1         5     1      0       I
17     1 1         2     1      1       I
18     1 1         4     1      1       I
19     0 1         2     1      1       R
20     1 1         6     1      1       R
21     8 0         4     1      0       R
22     3 0         3     1      1       D
23     2 1         3     1      0       I
24     5 1         2     0      0       D
27     4 0         2     1      0       D
28     0 0         3     1      1       I
29     8 1         3     1      1       D
30     5 1         3     1      0       R
31     0 0         1     0      1       D
32     4 1         5     1      0       R
33     5 1         4     1      0       I
34     8 1         3     1      0       R
35     5 0         3     1      0       I
36     1 1         5     1      1       I
37     1 0         6     1      1       R
38     5 0         1     1      1       D
39     2 0         3     1      1       R
40     1 1         6     1      1       R
41     5 0         3     0      0       I
42     2 0         1     1      1       D
43    10 0         3     1      1       D
44    10 1         5     1      1       R
46    10 0         0     1      0       R
47     8 1         0     1      0       D
48     7 1         5     1      0       R
49     5 1         3     0      0       D
50     4 1         3     1      1       R
52    10 1         6     1      0       R
53     3 1         3     1      0       I
54     5 1         1     1      0       R
55     3 0         6     1      0       R
57     1 1         3     0      0       D
58     2 1         2     1      1       I
59     6 1         6     1      1       D
60     0 0         5     0      0       D
61    10 1         0     0      0       R
62    10 0         3     0      0       R
64     4 1         3     1      1       D
66     0 0         0     1      0       D
68    10 0         0     1      1       D
69     4 1         2     1      0       D
70    10 1         6     1      1       R
71     8 0         5     1      0       R
72     4 0         3     0      0       I
74     7 1         5     1      1       D
75    10 1         3     1      0       I
76     6 1         1     1      0       R
77     6 1         2     1      0       D
78     7 1         2     1      1       D
79     6 0         1     0      0       R
80     8 0         2     0      0       I
82     4 0         2     0      0       D
83     0 1         5     0      0       D
85     1 1         1     1      1       D
87    10 1         3     1      1       R
89     2 0         1     1      1       D
90     6 1         6     1      0       R
91     7 1         1     1      1       D
92     8 0         6     1      1       R
93     0 1         3     1      1       I
94     5 0         1     0      1       D
95     7 1         1     1      0       D
96     6 0         1     1      1       D
97     2 1         3     1      1       I
99     4 0         1     1      0       R
100    8 1         4     1      1       R
102    9 1         5     1      0       R
103    8 1         5     0      1       D
104    2 0         3     0      0       I
105    0 0         0     1      1       D
109    0 0         1     1      0       D
110    0 1         0     1      1       D
111    0 1         0     1      1       D
112    5 1         3     0      1       R
113    9 1         3     1      0       I
114    5 1         3     1      0       R
115   10 0         0     1      1       R
116    3 1         3     1      1       D
117    7 0         4     1      1       R
118    5 1         3     1      1       R
119   10 0         3     1      0       R
120    5 0         5     1      0       R
121    5 0         4     1      0       R
123    8 1         4     1      1       I
125    0 1         3     1      0       D
126    2 1         3     0      1       D
127    1 1         3     1      1       I
128    9 0         1     0      1       D
129    2 0         5     1      1       R
130    3 1         5     1      1       R
131    3 0         3     0      1       D
132    4 1         3     1      1       I
134    0 1         3     1      0       R
136    5 0         3     0      1       D
137    5 1         6     1      0       R
138   10 1         5     1      0       I
139    6 0         5     0      0       D
140    1 1         3     1      1       D
142    7 0         4     1      0       R
144    0 0         0     1      1       I
145    5 1         0     0      0       R
147    2 1         2     1      1       I
148   10 1         4     1      0       R
149    3 1         5     1      1       R
151   10 1         5     1      1       R
154    0 1         4     1      0       I
155   10 1         5     0      1       R
156    5 1         1     1      0       D
157    8 1         4     1      1       D
158   10 1         3     1      1       D
159    6 1         6     1      1       R
160    0 1         5     1      1       R
161    0 1         3     1      1       I
162    6 1         2     1      1       I
164    3 0         3     1      0       I
166    8 0         1     0      0       I
167    6 1         1     1      1       D
168    4 1         2     1      1       D
170   10 1         4     1      1       R
171   10 1         6     1      1       R
172    2 0         5     1      1       R
175    7 1         3     0      1       D
177   10 1         6     1      1       R
178    2 0         3     1      0       D
179    0 1         5     1      1       R
180    1 1         2     1      1       D
181   10 1         5     0      0       I
182    8 0         3     1      1       I
183    5 0         6     1      0       R
184    0 0         1     1      0       D
185    5 0         3     0      1       D
186    5 0         6     1      1       D
191    5 0         6     0      0       R
192    3 0         3     1      1       D
193    8 1         2     1      1       I
194    5 1         4     1      1       R
195    5 1         4     1      1       R
196    5 1         2     1      1       R
197    3 0         1     1      1       D
199    1 1         2     1      0       D
200    7 1         3     1      1       R
203    4 1         6     1      0       R
204    1 1         5     1      1       R
205    1 0         0     1      1       D
208    1 0         3     1      1       D
209   10 1         6     1      1       R
210    5 1         2     0      1       I
212    2 1         4     1      0       R
213    6 1         1     0      1       R
214    5 0         5     1      1       R
216    0 1         0     0      0       D
217    1 0         3     1      1       D
218    1 1         2     1      0       I
219   10 1         2     0      1       R
220    7 1         3     0      0       D
221    1 1         0     1      0       D
223    7 1         3     1      0       I
224    4 0         2     1      1       D
225    4 1         6     1      1       R
226   10 0         6     1      0       R
227    2 0         1     1      1       D
228    0 1         0     0      1       D
229    5 0         3     0      1       I
230    4 1         3     1      1       R
231    8 1         5     1      0       I
234    2 0         1     1      1       D
235    0 1         3     1      0       I
236    1 1         6     1      1       R
237    4 1         2     1      0       D
238    6 1         5     1      1       D
239    6 1         5     1      1       R
240    6 0         4     1      1       D
241    4 1         5     1      0       R
242    5 0         5     1      1       R
243    1 1         3     1      1       R
244    5 1         2     0      1       D
245    2 1         5     1      0       R
246    3 0         3     1      1       D
247    3 1         5     1      1       R
248    0 0         1     1      1       D
249    2 0         3     1      1       D
250    7 1         5     1      1       R
251    9 0         6     1      1       R
253    7 1         2     1      1       D
254    6 1         6     1      1       R
255    3 1         3     1      1       D
256    4 1         5     1      1       D
257    2 1         3     1      1       R
258    8 0         5     1      0       R
259    6 0         1     0      0       R
260    0 0         4     0      0       R
261    1 0         1     1      0       D
262    5 1         6     1      0       R
263    5 1         6     1      1       R
264    1 0         2     1      1       D
265    0 1         1     1      1       D
266    2 0         4     1      1       I
267    6 0         5     1      0       R
269    0 0         4     1      1       R
270    3 1         5     1      1       R
271    0 1         2     1      1       R
272    0 1         3     0      1       D
273    8 1         6     1      0       R
274    4 0         3     1      1       D
275    8 0         3     1      1       R
276    3 1         1     0      0       I
278    5 1         3     0      1       R
280    5 1         1     1      0       D
281    5 1         3     1      1       R
282    8 1         6     1      1       R
283    3 1         4     1      1       R
284    3 1         3     1      1       D
285    1 0         3     1      1       D
286    0 1         3     1      1       R
287    1 1         1     1      0       D
288   10 1         5     1      1       R
289    0 1         1     1      1       D
290   10 1         1     1      0       D
291    2 0         3     1      0       I
292    3 1         0     1      0       D
293    3 1         3     1      1       R
294   10 1         3     1      1       R
296    1 0         5     1      0       I
299    0 0         3     1      1       D
300    4 0         5     1      1       R
301    7 0         6     1      0       D
302    5 1         6     1      0       R
303    1 0         1     1      0       D
305    2 1         5     1      1       R
306   10 0         1     1      0       D
307   10 0         5     1      1       R
308    0 0         1     1      0       D
309    1 0         1     1      1       D
311   10 1         1     1      0       D
312    1 1         2     1      1       I
314    9 1         4     1      0       I
315    0 1         0     1      0       D
316    2 1         5     1      1       I
317    3 0         1     1      1       D
320    5 1         4     1      1       I
321    1 1         3     1      0       I
322   10 1         0     1      0       R
324    8 1         6     1      1       R
325    5 1         1     1      1       D
327    0 0         1     1      1       D
328   10 1         5     1      0       R
329    1 0         5     1      0       R
330    2 1         3     1      1       R
331    5 0         0     0      0       D
332    8 1         2     1      0       D
333    2 1         3     1      0       I
334    7 0         3     1      1       I
335    2 0         1     1      0       I
336    2 1         1     1      0       D
337    4 1         5     1      1       R
338    3 1         2     1      1       D
340    2 0         1     1      1       D
342    9 1         3     1      1       I
343    5 1         1     1      1       D
345    8 0         3     1      1       R
346    4 1         5     0      1       D
347    5 1         1     0      1       D
348   10 1         0     1      1       D
349    1 0         5     1      1       R
350    6 1         3     1      1       I
351    1 0         2     1      1       I
352    1 0         5     1      1       R
353    8 0         1     1      0       D
354    0 0         3     0      1       D
355   10 1         3     1      0       I
356    1 1         5     1      1       I
358   10 1         6     1      0       R
359    0 0         1     1      1       D
361    5 0         1     0      0       D
362    5 0         3     1      0       I
363    9 0         5     1      1       R
364   10 1         3     1      1       R
366    7 1         3     1      0       I
367    1 0         4     1      1       D
368    2 1         4     1      1       R
369    7 1         6     0      0       R
370   10 0         6     1      0       R
371    8 1         0     0      0       D
372    6 0         5     1      0       I
373    0 1         5     0      1       R
374    4 1         3     1      1       D
375   10 1         2     1      1       I
376    0 1         3     1      1       D
377    2 1         5     1      1       R
378    4 0         1     1      0       D
380    0 1         3     1      1       D
381    4 1         6     1      1       R
382    0 0         0     1      1       D
383    2 1         3     1      1       R
384    7 1         4     1      0       I
385    2 0         0     1      1       D
386   10 1         3     1      1       R
388    9 1         3     1      1       I
389    0 1         6     1      1       R
390    6 1         6     0      0       R
391   10 1         5     1      0       R
394    7 1         4     1      0       D
395    5 0         2     0      1       D
396    0 1         3     1      1       I
397    1 0         5     1      0       R
398    2 1         5     1      1       I
399    0 1         5     1      1       R
400    6 0         6     1      0       R
401    6 1         3     1      1       D
402    6 1         4     1      0       R
403    8 1         1     1      0       D
404    6 0         3     1      0       D
405    0 0         3     1      0       I
406    5 1         1     1      1       D
407    2 1         4     1      0       R
408    9 1         3     1      1       D
410    9 0         5     0      1       D
411    3 1         3     1      1       R
413    4 1         3     1      1       R
414    1 0         0     1      1       D
415    5 0         5     1      1       R
416    1 1         0     1      0       D
417    4 0         5     0      0       I
418    9 0         0     0      1       D
420    8 1         3     1      1       R
422    3 1         2     1      0       I
424    9 0         3     0      0       I
425    4 1         5     1      0       R
426    8 0         3     1      1       I
427    5 0         6     1      1       R
428    7 1         6     1      0       R
429    8 1         0     1      0       I
430    3 1         3     0      1       D
431    7 1         5     1      1       R
432    2 0         3     1      1       I
433    3 1         3     1      1       I
434    3 1         5     1      1       I
435    3 1         5     1      1       R
436    0 0         1     1      0       D
437    0 1         1     1      0       D
438    2 1         2     1      0       D
439    5 1         6     1      1       R
440    5 0         3     1      1       I
441    2 1         0     1      1       D
442    0 0         2     1      1       D
443    2 0         4     1      1       I
444    9 1         2     1      1       I
445    7 0         5     1      1       R
446    1 0         1     1      1       D
447    2 1         6     0      1       R
448    5 1         1     1      0       D
449    5 0         0     1      0       D
450    3 1         4     1      0       R
451    0 1         3     1      1       I
452    1 1         5     1      0       R
453    5 1         5     1      0       R
454    1 1         5     1      0       R
455    4 1         3     0      1       D
457    5 1         5     1      1       R
458   10 1         6     1      1       R
459    8 1         2     1      0       R
460    3 1         5     1      1       R
461    1 1         0     1      1       D
463    5 1         3     0      0       I
464    8 0         3     1      1       R
465    5 0         3     0      1       D
466    2 0         3     1      1       I
467    7 1         3     0      1       D
469    3 1         3     1      0       I
470    2 1         5     1      1       R
471    1 1         1     1      1       D
472    2 0         5     1      1       R
473   10 0         5     1      1       I
474    2 1         1     1      1       D
476    0 1         1     1      1       D
477    6 1         6     1      1       R
478    5 0         6     1      0       R
480    2 1         3     0      1       D
482    5 1         5     1      0       R
483    5 1         4     1      1       R
484    5 1         5     1      1       R
485    3 1         4     1      1       I
486    5 1         3     0      1       D
487    2 1         0     1      0       D
488   10 0         3     1      1       I
489    3 1         5     1      1       R
490    5 0         3     1      1       D
492    3 0         3     1      0       D
494    5 1         3     1      1       I
495    5 1         1     0      1       R
496    4 1         5     1      0       R
498    0 0         3     1      1       D
499    3 0         4     1      1       R
501    4 1         3     1      0       D
502    6 1         2     1      1       D
503    8 0         1     1      0       I
504   10 1         1     1      1       I
505    4 0         6     0      0       D
506    3 1         1     0      1       D
507    1 0         0     1      1       D
508    5 0         3     1      1       I
509    1 1         1     1      1       D
510    5 0         3     1      1       R
511    1 1         4     1      1       I
512    2 0         1     1      1       D
513    2 1         3     1      1       D
514    0 1         3     0      1       D
515   10 1         1     1      0       D
516    8 0         1     0      0       D
517    0 1         3     0      0       D
518    3 0         6     1      1       R
519    2 1         1     1      1       D
520    5 1         6     1      0       I
521    1 0         3     1      1       I
522    7 1         1     0      1       D
523    7 1         3     1      1       D
524    3 1         6     1      1       R
525    4 1         5     1      1       R
526    6 1         3     1      1       D
528    7 1         2     1      1       D
529    7 1         4     1      1       R
530    7 1         5     1      1       I
531    3 0         5     1      1       R
532    3 1         2     1      1       I
533    2 1         3     1      0       I
534    4 0         3     1      1       R
535    3 1         3     1      1       R
536   10 1         5     1      0       R
537    9 0         6     1      1       R
538    5 1         3     1      1       R
539    2 0         4     1      1       R
540    0 1         3     0      0       R
541   10 1         4     1      1       I
542    4 1         4     1      1       R
543    3 0         2     1      0       I
544    5 1         1     1      0       R
545    8 1         3     0      1       D
546    9 0         3     0      1       I
547    1 0         1     1      1       D
548    0 0         1     0      1       I
549    4 0         3     1      1       D
550    5 1         5     1      0       R
551    6 0         3     1      1       I
552    3 0         0     1      1       D
553    5 0         3     0      1       I
554    5 0         3     1      1       I
555    4 1         5     1      1       R
558    4 1         1     1      1       D
559    7 0         4     1      0       D
560    3 1         5     1      0       R
561    3 0         3     1      0       D
562    8 1         5     1      1       R
563    3 0         4     1      1       D
564    2 1         4     1      1       I
565    1 0         4     1      1       R
566    7 1         3     1      1       I
567   10 1         6     1      1       R
569    1 1         5     1      0       R
570    5 1         6     1      1       R
571    7 1         5     1      1       R
572    7 1         3     0      1       D
573    0 0         0     1      1       D
574    7 1         1     1      0       D
575    7 1         3     1      1       I
576    5 0         2     1      1       D
577    2 0         4     1      0       R
578    5 0         2     0      1       I
579    0 1         3     1      1       D
581    0 0         6     1      1       D
582    0 1         1     1      1       D
584    0 0         0     1      0       D
585    7 1         2     1      0       I
586    2 0         2     1      1       R
588    4 0         3     1      0       D
589   10 0         0     1      0       R
592    4 1         3     1      1       R
593    8 1         5     0      1       R
594    0 0         1     1      0       D
595    5 0         3     1      1       I
596    8 1         3     1      0       I
597    5 0         0     1      0       I
599    5 0         1     0      1       D
600    5 1         3     1      0       D
601    2 0         3     1      1       I
602    2 0         1     1      1       D
604    1 0         4     1      0       R
605    1 1         5     1      1       R
607    5 1         4     1      1       R
608   10 1         1     1      1       D
609    1 1         3     1      1       I
610   10 0         3     0      0       D
611   10 0         4     1      0       R
616    4 1         2     1      1       I
617    8 1         3     1      1       D
618    1 1         5     1      1       R
620    3 1         3     1      1       R
621    3 1         5     1      0       R
622    6 1         5     1      1       R
623    8 1         4     1      1       D
624    4 0         2     1      1       R
625    2 1         2     1      1       D
626   10 0         3     1      0       R
627    2 1         2     1      1       D
628   10 1         3     1      1       I
629    5 1         3     1      1       R
630    4 1         3     1      0       I
631    2 0         3     1      1       R
632    2 1         1     1      1       D
633    6 0         2     0      0       D
634    0 1         5     1      0       R
635    5 1         1     1      1       I
637    1 1         2     1      0       D
638    6 1         3     1      1       R
639    1 0         6     1      1       I
640    3 1         1     0      1       I
641    2 0         5     1      0       R
643    0 0         3     1      1       I
644    2 0         1     1      1       I
645    1 0         1     1      0       D
646    1 1         6     1      0       R
647    1 0         1     1      1       D
649    6 1         5     0      0       R
650   10 0         3     0      0       I
651    5 1         3     1      0       I
653    7 1         4     1      1       R
655    0 1         0     1      1       D
656    2 1         4     1      0       I
657    3 1         3     0      1       I
658    4 0         2     1      1       D
660    3 1         3     0      1       I
661    4 1         5     1      1       R
662    5 0         3     0      0       I
663    1 1         3     0      1       D
664    1 0         1     0      1       I
665   10 1         1     0      1       R
666    1 1         3     1      1       I
667    8 1         5     1      1       R
669   10 0         1     1      1       R
671   10 1         6     1      1       R
672    8 1         3     1      1       D
673    1 1         1     1      1       D
674    4 1         3     1      1       I
675    6 0         1     1      0       D
676    5 1         5     1      1       R
677    1 0         3     0      0       R
678    4 1         0     1      1       D
679    7 1         3     0      1       D
680    5 0         1     1      1       R
681   10 1         3     1      1       R
683    8 1         3     1      0       D
684    3 1         1     1      1       D
686   10 0         6     1      1       R
688   10 1         6     1      1       R
689    2 0         4     1      1       I
690    1 0         1     1      1       D
691    4 0         3     1      1       D
693    3 0         6     1      0       R
694    0 0         3     0      0       D
695    2 1         3     1      1       R
696    7 1         3     1      1       R
697    0 1         3     0      1       I
698    4 1         1     0      1       D
699    9 1         6     1      0       R
701   10 0         6     1      1       R
702    7 1         5     1      0       R
703    0 0         0     1      1       D
704    1 1         5     1      0       R
705    2 0         2     1      0       D
706    3 1         3     1      1       D
707    0 1         4     1      1       R
708    8 1         3     1      1       D
709    5 0         1     1      0       R
710    5 1         1     0      0       I
711    5 1         5     1      0       R
712    2 1         1     0      1       D
713   10 0         2     0      1       D
714    5 1         3     0      1       D
715    4 1         3     1      1       I
716    2 0         3     1      0       D
718    0 0         3     1      1       I
719    0 1         0     1      1       D
720    7 1         3     1      0       D
721    7 1         2     0      1       I
722    5 1         3     1      1       D
723    3 0         5     1      0       I
725   10 1         6     0      1       D
726   10 1         6     1      0       R
727    4 1         5     0      0       I
728    0 0         1     1      0       D
729    0 1         6     1      1       R
730    4 1         5     1      0       R
731    6 0         2     1      1       R
732    5 1         0     0      1       D
733    4 1         5     1      0       D
734   10 0         1     1      1       D
736    0 1         0     0      1       D
737    7 1         1     1      1       D
738    7 1         1     1      1       D
739    1 1         2     1      1       I
741    7 0         5     1      0       R
742    1 1         1     1      1       D
744    5 1         2     1      0       R
745    5 1         4     1      0       D
746    0 0         6     1      0       R
747   10 1         5     1      1       I
748    8 1         2     1      1       D
749    2 1         2     0      0       I
750    5 0         3     1      1       D
752   10 1         6     1      1       R
753    8 1         6     1      1       R
755    1 1         2     1      1       D
756    1 1         3     1      1       D
757    4 1         1     0      1       I
759    5 1         2     1      1       D
760    8 1         0     0      1       D
762    2 0         0     1      1       D
763   10 0         4     1      1       I
764    0 0         1     1      0       D
765    5 1         6     1      0       R
766    6 0         3     0      1       D
767    7 0         1     1      0       D
768    0 1         5     1      0       R
770    5 1         4     0      1       R
771    5 1         6     1      0       R
772    6 0         4     0      0       D
773   10 0         6     1      0       R
774    5 1         2     0      1       R
775    2 0         5     1      0       R
776    1 1         3     0      1       D
777    1 1         6     0      0       R
778   10 0         5     1      0       I
779    5 1         4     1      0       R
780    5 1         6     1      1       R
781    5 1         3     0      1       D
782    4 0         5     1      1       R
783    2 1         0     1      1       D
784    2 1         2     1      1       I
785    5 1         2     1      1       I
786    0 0         1     0      0       D
787    0 1         3     1      0       I
788    4 1         5     1      0       R
789    3 0         2     1      1       D
790    3 1         2     1      0       D
791    9 1         5     1      1       R
792   10 1         6     1      0       R
794    7 1         3     1      1       D
795    4 1         4     1      1       R
796    6 1         4     1      1       D
797    4 1         1     1      0       D
798    5 1         2     0      1       I
799    2 0         3     1      0       I
800    0 1         1     1      1       D
801    5 1         6     1      1       I
802    4 1         5     1      1       I
803    0 1         6     1      0       R
806    2 0         1     1      0       D
807    1 1         3     1      1       R
808    3 0         5     1      1       R
809    5 1         5     1      1       R
810    4 1         1     1      1       D
811    6 1         3     1      1       D
812    5 1         5     1      1       R
813   10 0         6     1      1       R
814    1 1         3     1      1       I
816    0 1         1     1      1       D
817    9 1         0     0      0       R
818    5 1         1     1      1       D
819    2 1         1     0      1       D
820    1 0         5     1      1       R
821    0 1         6     1      0       R
822    0 0         5     0      1       D
823    2 1         4     1      1       I
824    2 0         5     1      1       R
825    1 1         1     1      1       D
826   10 1         3     1      1       D
827    8 1         3     0      1       D
828    5 0         3     0      1       D
829    0 1         3     1      1       D
830    2 1         1     1      1       D
831    0 0         3     1      1       I
832   10 1         3     1      1       R
833    2 1         3     1      0       I
835    9 1         5     1      0       R
836    4 1         0     1      0       D
837    3 1         3     1      0       I
838    2 0         5     0      1       D
839    0 0         0     1      1       D
840    6 1         3     1      1       R
841    2 1         4     1      0       I
842    3 1         3     1      0       D
843    9 0         5     0      1       R
844    7 1         5     0      1       R
845    2 1         5     1      1       R
846    3 1         5     1      1       D
847   10 0         3     1      1       D
848    5 1         3     0      1       I
849    1 0         1     0      1       D
850    5 1         5     1      1       R
851    5 1         3     1      0       D
852    0 0         3     1      1       I
853    3 1         2     1      1       D
855    6 1         2     1      0       D
856    8 1         2     0      1       I
857    2 0         6     1      0       R
858    1 0         3     1      1       D
861    1 0         6     1      1       R
862    6 1         4     1      1       R
863    1 0         3     1      1       I
866    4 1         5     1      1       R
867    0 1         4     1      1       I
868    5 1         3     1      1       I
869    1 1         3     1      0       I
872    9 1         6     1      0       R
873    5 1         2     1      1       D
874    7 0         6     1      1       R
875    2 0         6     1      0       R
876    7 0         3     0      1       D
878    1 1         1     1      1       D
880    0 0         6     1      1       R
881    3 0         6     1      1       R
882    2 1         3     0      0       D
883    9 1         5     0      1       D
884    7 0         3     1      0       D
885    8 1         1     0      1       D
886    0 0         3     0      1       D
887    1 1         3     1      1       D
889   10 1         3     1      1       I
891    1 1         4     1      1       R
892    2 1         2     0      1       D
893    1 1         1     1      0       D
895    6 0         4     1      1       I
896    0 1         6     1      1       R
897    2 1         3     0      0       D
898    3 0         4     1      1       R
899    3 1         5     1      0       I
901    6 1         6     1      1       D
902    0 0         4     1      1       R
903   10 0         3     1      0       D
904    5 0         5     1      0       R
905    0 1         3     1      1       D
906    8 1         3     1      1       R
907    6 1         4     1      1       D
908    7 1         6     1      1       D
909    3 0         3     1      1       D
910    5 0         4     1      0       R
911    2 0         3     1      0       I
912    8 1         6     1      1       R
913    2 0         4     1      0       I
914    3 1         2     0      1       D
915    4 1         0     0      1       R
916    1 0         5     1      1       I
917    5 0         3     1      0       I
920    7 1         2     1      1       I
922    5 0         4     1      0       R
923    8 1         1     0      0       D
924    5 0         5     1      1       I
925    2 0         3     1      1       R
926    3 0         6     1      1       R
929    5 1         6     1      1       R
931    2 1         2     1      1       D
932    5 1         4     1      1       R
933   10 0         6     1      1       I
934    7 1         6     1      1       I
935   10 1         5     1      0       R
936   10 1         3     1      1       D
937    4 0         1     1      1       D
938    2 1         3     1      1       I
939    0 1         3     1      0       I
940    3 1         5     1      1       I
941    4 1         5     1      0       R
942    9 1         3     1      0       D
943    5 0         4     1      0       R
944    3 1         0     0      1       D
946    0 0         1     1      0       I
947    1 1         3     1      1       I
948    5 1         3     1      1       I
949    8 0         4     1      1       I
952    1 0         1     0      0       D
953    5 0         1     1      1       D
954    0 0         2     1      1       D
955    2 1         6     1      0       R
956    1 0         1     1      1       D
957    4 1         5     1      1       R
958    0 1         4     1      1       R
959    5 1         1     0      1       D
960    5 1         3     1      0       D
962    4 0         3     0      0       D
964   10 1         3     1      0       R
965    3 1         5     1      1       R
966    3 1         4     1      1       R
970    4 0         3     1      1       R
973    3 1         2     0      1       D
974    0 0         3     1      0       I
975    5 0         3     1      0       I
977    0 0         1     0      1       D
979    3 1         4     1      0       R
981   10 1         3     1      1       R
983    7 0         1     1      1       D
985    5 1         3     1      1       I
988    4 1         1     0      0       D
989    3 0         0     1      0       D
990    2 0         5     1      1       D
991    7 1         3     1      1       R
992    2 0         5     0      0       D
993    7 1         3     1      0       I
994    5 1         1     1      1       D
995    3 1         5     1      1       R
996    0 0         1     1      1       D
998    6 1         2     1      1       R
999    2 0         0     1      1       D
1000   4 0         3     0      0       R
1001   8 1         4     1      1       R
1002   0 0         2     1      0       D
1003   1 1         5     1      1       R
1005   0 1         1     1      1       D
1006   8 0         3     0      0       R
1007   1 1         4     0      0       D
1008   0 1         3     1      1       D
1009   8 1         3     0      0       D
1010   5 0         1     0      0       D
1014   0 1         1     1      1       D
1015   1 1         5     1      1       I
1016   0 0         3     1      1       I
1017  10 1         1     1      1       D
1019   6 0         3     1      1       I
1020  10 0         1     0      0       I
1021   1 0         1     1      1       I
1022   5 0         3     1      0       R
1023   3 1         5     1      0       R
1024   3 0         5     0      0       I
1025   6 0         3     1      0       I
1026   8 1         3     1      1       I
1029  10 1         6     1      0       R
1030   2 0         3     1      1       I
1031   2 1         2     1      1       D
1032   5 1         3     1      1       D
1033   1 1         3     1      1       D
1034   0 1         1     1      0       D
1035   8 1         6     1      1       R
1037   5 0         3     1      1       R
1038  10 1         6     1      1       R
1040   0 1         1     1      0       I
1041   3 0         4     1      1       R
1042   0 1         1     0      1       D
1043  10 1         3     1      1       R
1044  10 1         5     1      0       R
1046   5 0         6     1      0       R
1047   1 1         4     1      1       R
1049   0 0         2     1      1       D
1050   5 1         4     1      1       R
1051   0 1         3     1      1       D
1053   3 0         3     1      0       R
1054   5 1         1     0      0       I
1055   2 1         5     1      1       R
1056   5 0         5     1      1       I
1057   2 0         1     1      1       D
1058   9 1         0     1      0       I
1059   0 0         4     1      0       R
1060   7 1         2     1      1       R
1062   8 1         5     1      0       R
1063   6 1         5     1      1       R
1064   1 1         4     1      1       R
1065   3 0         3     0      0       I
1066   6 1         6     1      1       R
1067   6 1         3     0      0       I
1068   0 1         1     0      1       D
1073   6 1         3     0      1       D
1074   0 1         1     1      1       D
1076   3 1         1     1      0       D
1077   5 0         5     0      1       R
1078   5 0         3     1      1       I
1079   0 0         5     1      0       R
1080   0 1         5     1      0       R
1081   2 1         5     1      0       R
1082   1 1         0     1      1       D
1083   5 1         4     1      0       D
1084   3 1         3     1      0       D
1085   3 0         3     1      0       D
1086   0 1         3     0      1       R
1087  10 1         3     1      1       R
1088   3 1         3     1      1       R
1089   5 1         6     0      1       D
1090   3 1         2     1      0       R
1092   1 1         5     1      1       R
1093   4 1         2     1      0       D
1094   1 1         1     1      1       D
1095   2 0         3     1      1       I
1096   1 1         3     1      1       R
1097   1 1         3     1      1       D
1098   6 1         2     0      1       D
1100   1 0         5     1      0       R
1101   7 1         5     1      1       R
1102   0 0         3     1      0       D
1104   9 1         5     1      1       I
1105   8 1         5     1      0       R
1107   1 1         5     1      1       R
1108   7 1         3     1      1       D
1109   3 0         3     1      1       D
1110   7 1         3     1      0       D
1111   2 1         1     1      1       D
1112   1 1         3     0      0       I
1113  10 0         0     1      1       D
1114   5 1         1     1      1       D
1115   6 1         0     1      1       D
1116   5 1         5     1      1       R
1117   6 1         3     0      1       I
1120  10 1         6     1      1       R
1121  10 1         3     1      1       D
1122   8 0         0     1      1       R
1124   4 1         5     1      1       R
1125   7 1         5     1      1       I
1126   2 0         2     1      1       I
1127   5 0         1     1      0       R
1128  10 1         6     1      1       R
1129  10 1         3     1      1       D
1131   7 1         2     0      1       I
1132   5 0         4     1      1       D
1133   5 1         3     1      1       I
1134   6 0         4     1      0       I
1136   2 0         4     1      1       R
1137   5 1         1     0      1       D
1138   6 1         3     1      1       R
1139   2 0         3     0      1       D
1140   3 1         0     0      1       I
1141   5 1         3     0      0       I
1142   1 1         6     1      1       R
1143   2 0         3     0      0       I
1144   5 1         5     1      1       R
1145   5 1         3     1      0       D
1147   1 1         4     1      1       R
1148   2 1         2     1      1       D
1149   9 1         3     1      1       R
1150   5 0         3     1      0       I
1151   3 0         3     1      1       I
1152   5 1         5     1      1       R
1153   8 1         4     0      0       D
1154   2 1         3     0      0       D
1155   1 0         3     1      0       D
1156   5 0         5     1      0       R
1157  10 1         3     0      0       D
1158   4 0         3     1      1       I
1160   2 1         4     1      1       R
1161   8 1         6     1      1       R
1162   1 0         4     1      0       I
1163   0 0         1     0      1       D
1164   3 1         3     1      1       I
1165  10 0         3     1      1       R
1167   0 0         3     1      0       R
1168  10 1         6     1      1       R
1169   1 1         4     1      1       R
1170   5 1         3     1      0       I
1171   4 1         1     1      1       D
1173   5 1         2     0      1       I
1174   5 1         3     1      1       I
1175   9 1         2     0      0       R
1176   0 1         0     1      0       D
1178   2 1         1     1      1       R
1179   4 0         1     0      0       D
1180   5 1         3     1      0       D
1181   0 1         1     0      1       I
1182   2 1         4     1      0       D
1183   2 0         1     1      0       D
1186   5 1         4     0      0       D
1187   6 1         1     0      0       I
1188   1 0         3     0      0       I
1189   1 1         6     1      1       R
1191   3 1         3     1      1       I
1192   5 0         2     1      1       D
1193   2 1         1     1      0       D
1195   4 1         1     0      1       I
1196   5 1         3     1      0       D
1197   0 0         2     1      1       I
1198   8 1         4     0      0       R
1200   2 1         3     1      1       I
1201   3 0         1     1      1       D
1202   7 0         3     1      0       I
1205   3 1         3     1      0       D
1206   9 1         1     0      0       R
1207  10 1         5     1      1       R
1208   6 0         3     0      1       D
1210   0 1         1     0      1       D
1213   6 1         1     1      0       R
1214   6 1         1     0      1       I
1218   6 1         5     0      0       R
1219   2 1         3     1      1       I
1220   7 0         3     0      1       R
1222   2 1         2     0      1       D
1225   5 0         0     0      1       D
1227   2 0         3     0      1       I
1228   7 1         4     0      0       R
1229   5 0         5     0      0       I
1230   5 1         4     0      1       R
1231   7 1         5     0      0       D
1233   1 1         3     1      0       I
1235   5 1         1     0      0       D
1237  10 1         0     0      0       D
1238   0 0         0     0      0       I
1239  10 1         5     0      0       R
1240   4 0         3     0      1       D
1242   9 0         3     0      1       I
1243  10 0         2     0      0       D
1244   7 1         4     0      0       R
1245  10 0         1     1      0       D
1246   4 0         6     0      0       R
1249   0 1         0     0      0       D
1250  10 1         4     1      0       R
1252   3 1         1     0      0       D
1253   9 0         3     1      1       R
1254   7 1         3     0      1       D
1255   8 0         6     1      0       D
1256   0 0         1     0      1       D
1257  10 1         1     0      0       I
1258   3 0         0     1      0       D
1259   6 1         1     0      1       D
1261   0 0         3     0      1       D
1262   8 1         5     1      0       D
1263   5 1         1     0      1       D
1264   9 0         3     0      1       R
1266   2 1         0     1      1       I
1268   1 1         1     1      0       D
1269   5 1         1     0      0       D
1270   6 0         0     0      0       D
1271   4 0         5     1      0       D
1274   5 1         0     0      0       R
1276   7 1         2     0      1       D
1277   3 1         2     0      0       R
1278  10 1         2     0      1       D
1280   1 0         1     0      1       D
1283   7 1         1     0      1       D
1284   7 0         3     0      0       D
1285   9 1         4     0      0       I
1286  10 0         2     0      0       D
1287   0 0         5     0      0       D
1288   4 0         1     1      1       D
1292   6 1         0     0      0       D
1293   1 1         3     0      1       D
1294   2 0         2     0      1       D
1295   6 0         1     0      0       D
1296   8 1         3     0      1       D
1297   5 0         2     0      1       D
1298   7 0         3     0      1       I
1299   4 1         3     0      1       I
1300   8 1         1     0      0       D
1301   3 0         5     1      1       R
1302   6 1         5     0      0       I
1303   0 0         3     1      0       D
1304   2 1         0     1      1       D
1305   7 1         3     0      1       D
1306   4 1         1     0      1       I
1309  10 1         6     0      0       R
1310   7 1         3     1      1       I
1311   8 1         1     0      0       D
1313  10 1         1     0      0       D
1314   0 1         1     0      0       R
1315   3 1         3     0      0       D
1317   0 1         1     0      1       D
1318   0 1         4     0      1       D
1319   8 1         5     1      0       R
1320  10 0         3     1      0       R
1321   8 1         4     1      0       R
1323  10 1         5     0      0       R
1324   8 1         5     1      0       R
1325   7 1         3     0      0       D
1326   6 1         5     0      0       R
1328   1 1         3     0      1       R
1329   7 1         0     0      0       D
1332   7 0         4     1      0       R
1333   7 1         1     1      0       D
1334   6 1         1     0      1       I
1335   3 1         3     0      0       I
1336   7 1         2     1      1       R
1338   0 1         0     0      0       D
1339   8 0         0     0      0       R
1341   5 1         0     0      1       D
1342   5 1         0     0      0       I
1343   5 1         1     0      0       D
1344   6 1         1     0      1       D
1345  10 0         1     0      1       I
1346   4 0         3     0      0       D
1349   0 1         0     0      1       D
1350   7 0         1     0      0       R
1351   5 1         3     0      1       D
1352   0 0         3     0      1       I
1353   8 1         1     0      0       D
1354   9 1         3     0      0       D
1357  10 1         2     0      1       D
1358   3 0         1     0      0       D
1359   2 1         4     0      0       D
1360   3 1         3     0      0       I
1361   3 1         0     0      1       D
1364   0 1         3     0      0       D
1365   5 0         3     1      1       I
1366  10 1         5     0      0       D
1370   3 0         3     0      1       D
1372   3 0         2     0      0       D
1373  10 0         0     1      0       R
1374   4 0         3     0      0       D
1376   9 0         1     0      0       D
1377   7 1         4     0      1       D
1378   4 1         2     0      0       I
1379   9 1         1     0      0       D
1382  10 1         1     0      0       R
1383   3 1         1     0      1       D
1384   5 1         0     0      1       D
1386   7 0         1     0      0       D
1387   6 1         1     1      0       D
1388  10 0         0     0      0       R
1389   5 1         1     0      0       I
1390   8 0         3     0      1       D
1391   8 1         1     0      0       D
1392  10 0         3     0      0       D
1393   5 1         3     0      0       I
1394   4 0         4     0      0       I
1395   0 1         3     1      0       I
1396   5 1         3     0      1       I
1397   7 1         3     0      0       D
1398   4 1         2     1      1       D
1402   7 0         2     0      1       I
1403   5 1         2     1      0       D
1404   6 1         3     0      0       D
1405   7 0         1     0      1       I
1406   8 1         0     1      1       R
1408   5 1         3     0      0       D
1409   0 1         0     1      0       D
1410  10 1         3     0      0       I
1412   7 1         1     0      0       D
1415   9 1         3     0      0       I
1416   8 1         3     0      1       R
1417   2 1         5     0      0       I
1418   5 0         3     0      0       D
1419   6 0         2     0      1       D
1421   6 0         2     0      0       I
1422   6 1         5     0      0       I
1423   6 0         1     0      0       D
1424  10 0         4     0      1       R
1425   6 1         5     0      1       D
1426   6 1         1     1      0       I
1430   0 0         0     0      0       D
1431   2 1         5     1      0       R
1432   5 1         5     0      0       R
1433   4 1         5     0      0       I
1437   5 1         2     0      0       R
1439  10 1         1     1      0       R
1441   6 0         1     0      1       D
1442   5 1         3     0      1       D
1443   7 1         3     0      0       D
1444   6 0         1     0      1       D
1446   8 1         4     0      1       R
1447   5 0         3     0      1       D
1449   3 1         4     0      0       D
1450   4 1         6     1      0       R
1451   5 0         1     0      0       I
1456   3 1         0     0      1       D
1458   3 0         2     0      0       I
1460   5 1         1     0      1       D
1461   0 1         3     1      0       I
1463   2 0         3     0      0       D
1465   7 1         5     1      1       I
1466   6 1         6     0      1       I
1467   2 1         4     1      0       I
1469   5 1         1     0      0       D
1471   9 1         1     1      0       D
1472   5 1         1     0      1       I
1473   6 1         1     1      0       R
1475  10 1         1     0      1       D
1476   4 1         1     0      1       I
1477   7 1         1     1      1       I
1478   4 1         2     0      1       D
1479   4 1         3     1      0       R
1480   4 0         3     0      1       I
1481   9 1         4     0      0       R
1482   4 1         3     0      1       D
1485   7 1         4     1      1       D
1486   1 1         1     1      1       D
1487  10 0         1     1      0       I
1488   9 1         5     0      1       I
1490   5 1         5     0      1       R
1491   9 1         3     1      0       D
1492   8 1         6     0      0       R
1494   3 1         0     0      1       D
1495   8 0         3     0      0       D
1496   4 1         1     0      0       D
1498   5 1         3     0      1       I
1500   4 1         3     1      1       D
1501   8 0         5     1      0       R
1503   3 1         6     0      1       R
1505   2 1         1     0      0       D
1506   9 0         1     0      0       D
1507  10 1         3     0      0       I
1511   7 0         3     1      0       R
1512   5 1         1     0      0       D
1513   2 1         3     0      1       D
1514  10 1         3     1      1       D
1515   1 0         3     1      0       I
1516   7 0         1     0      0       D
1517   5 1         3     0      1       I
1518  10 0         1     0      1       D
1519   6 1         0     0      0       R
1521   5 1         1     0      0       D
1522   6 1         0     0      0       R
1524   6 1         2     0      1       D
1525   5 0         3     0      1       D
1526   8 1         2     0      1       D
1527   1 1         1     1      1       D
1528   8 0         5     0      0       I
1529   0 1         1     1      1       D
1531   4 1         3     1      0       D
1532   7 0         1     1      0       I
1534   0 0         0     0      1       D
1536   8 1         5     1      1       R
1538   6 0         2     0      0       D
1539   6 1         3     0      0       D
1540   6 1         0     1      0       R
1541   7 0         4     0      0       I
1542   5 1         3     0      1       D
1543  10 1         1     1      1       R
1544  10 1         1     0      1       D
1545   5 1         1     0      0       D
1546   9 1         2     1      0       R
1547  10 1         3     0      0       D
1548  10 1         4     0      1       R
1549   1 0         3     1      0       R
1551   9 1         3     0      0       R
1552   8 1         4     0      0       R
1554   3 1         4     1      1       R
1555   0 1         1     0      1       I
1559   4 1         4     1      1       R
1560   5 0         3     1      1       D
1561   1 0         1     0      1       D
1564   7 0         5     0      0       R
1565   0 1         3     1      0       D
1566   5 0         3     0      0       D
1568   0 1         1     0      0       I
1569   3 1         3     0      1       I
1571   9 1         1     1      1       D
1572   9 1         5     0      0       D
1573   8 1         1     0      1       R
1574   5 1         3     1      0       I
1575   0 1         5     0      0       D
1576  10 1         3     1      1       I
1579   0 1         1     0      0       I
1581   4 0         3     0      1       D
1584   0 0         0     1      1       D
1585   5 1         5     0      1       I
1586   4 0         2     0      1       D
1587   9 1         4     0      1       D
1588  10 1         1     0      1       R
1590   6 0         3     1      1       D
1591   0 1         3     0      0       I
1592   7 0         3     0      0       D
1593   9 1         6     1      0       R
1594   3 1         3     1      0       D
1596   6 1         2     0      0       D
1597   1 1         3     1      0       I
1601  10 1         0     0      0       D
1602  10 0         1     1      0       R
1603  10 1         6     1      0       R
1604   1 1         2     1      0       I
1605   3 1         0     0      0       D
1606   8 1         1     0      0       D
1608   7 1         5     1      0       R
1609   9 0         5     1      0       R
1611   3 1         1     1      0       D
1612   8 1         5     0      0       R
1613   5 1         1     0      0       D
1614   8 1         2     1      1       I
1615   3 1         3     1      0       R
1616   5 1         1     0      0       D
1617   5 1         5     0      0       R
1618   0 1         3     1      0       R
1619   9 1         1     0      0       D
1620   8 0         1     0      0       D
1621   9 0         5     1      0       D
1622   2 0         2     1      0       D
1625   3 0         0     0      0       R
1626   7 0         1     1      1       D
1628  10 1         6     1      0       R
1629  10 0         6     1      0       R
1630   9 1         0     1      0       R
1631   9 0         4     0      0       R
1632   7 1         5     0      0       R
1633   5 1         4     1      0       R
1634   2 0         5     1      0       R
1635   3 1         1     0      0       I
1636   3 1         5     1      0       I
1637   6 0         6     0      0       I
1638   6 0         3     1      0       I
1640   5 1         3     0      0       I
1642   0 0         0     1      0       D
1643   5 1         0     1      0       R
1645   0 1         1     1      0       I
1647   5 0         6     1      0       R
1648  10 0         0     1      0       D
1650   1 0         4     1      0       R
1651   5 0         5     0      0       D
1652   9 0         2     0      0       I
1653   1 0         4     0      0       R
1654   8 1         5     1      0       R
1656   4 0         0     1      0       D
1657   6 1         2     0      0       D
1659  10 1         1     0      0       D
1660   3 0         4     1      0       R
1661  10 0         5     1      0       R
1663   8 1         1     1      0       R
1664   2 0         4     0      0       D
1665   6 1         5     1      0       R
1666   8 0         5     1      0       R
1668   0 1         1     0      0       D
1669   4 1         3     0      0       D
1671   6 1         4     1      0       R
1672   9 0         4     0      0       I
1673   6 1         3     1      0       R
1674   9 1         0     0      0       D
1676  10 1         5     1      0       R
1677  10 1         3     0      0       D
1678   7 1         2     0      1       D
1679   2 0         3     1      0       R
1680   5 1         1     0      0       D
1681   7 1         3     0      0       I
1682   8 1         1     0      0       D
1684   2 1         3     0      0       D
1686   7 1         2     1      0       R
1687   3 1         5     1      0       I
1689   1 1         6     1      0       I
1690   2 1         5     1      0       R
1693   0 0         4     1      0       D
1694   0 0         3     1      0       I
1695   0 1         0     0      0       D
1696  10 1         6     0      0       R
1697   0 0         3     1      0       R
1699   2 1         5     0      0       I
1700   8 1         5     1      0       R
1701   1 0         1     1      0       D
1702   8 1         0     0      0       I
1704  10 0         6     1      0       R
1705   4 1         4     1      0       R
1706   5 1         3     1      0       I
1707   5 1         1     1      0       D
1708   7 1         4     1      0       R
1709   7 0         3     0      0       D
1710   0 1         0     0      0       D
1711   2 1         2     1      0       D
1715   5 1         1     1      0       D
1716   7 1         1     1      0       D
1717   1 1         3     0      0       I
1718   3 1         0     1      0       I
1720   8 1         4     0      0       D
1721   2 1         0     0      0       I
1722   7 1         3     1      0       R
1723   7 1         1     1      0       R
1724   8 0         6     1      0       R
1725   9 0         2     0      0       D
1726   8 0         0     1      0       I
1728   1 1         5     1      0       D
1729   0 1         3     1      0       D
1731  10 1         0     1      0       R
1732   6 1         3     0      0       I
1733   2 0         5     1      0       R
1734   3 1         5     1      0       R
1735   5 1         1     1      0       D
1736   5 1         3     1      0       I
1738   0 1         5     1      0       R
1739   5 0         0     0      0       D
1740   4 1         3     1      0       I
1741   8 0         0     1      0       R
1744   1 0         1     1      0       D
1745  10 1         3     0      0       I
1746   0 1         3     0      0       D
1747   2 0         2     1      0       I
1749   2 0         1     0      0       D
1750  10 1         5     1      1       R
1751   0 0         3     0      0       D
1752   6 1         1     1      0       I
1753   6 1         3     1      0       R
1754   1 1         1     1      0       D
1755   5 1         4     1      0       R
1757   1 1         4     1      0       R
1758   6 1         3     1      0       R
1759   6 1         4     1      0       D
1761   6 0         2     1      0       D
1763  10 1         0     1      0       R
1764   7 1         3     0      0       I
1765   8 0         3     0      0       R
1766   1 0         3     0      0       D
1767   9 1         5     1      0       R
1769   9 0         4     0      0       I
1770   6 1         3     1      0       R
1771   0 0         2     1      0       I
1772  10 0         1     0      0       I
1773   5 1         0     1      0       R
1775   0 1         0     0      0       I
1776   6 1         3     1      0       I
1777   2 1         3     1      0       R
1778   1 1         3     0      0       I
1779   7 0         1     1      0       D
1781   8 0         0     1      0       R
1782   3 0         5     1      0       R
1783  10 1         6     1      0       R
1784   5 0         3     0      0       I
1787   7 0         1     0      1       D
1788   5 1         1     0      0       D
1789   7 0         1     1      0       R
1790   8 0         1     1      0       D
1791   9 1         2     1      0       D
1792   7 1         1     1      0       D
1793   7 0         1     1      0       D
1794   0 1         0     0      0       D
1795   0 1         2     0      0       D
1796   7 1         3     0      0       I
1797  10 1         0     0      0       D
1798   3 1         1     0      0       R
1799   8 1         5     0      0       I
1800   6 1         4     1      0       D
1802   7 1         4     0      0       D
1803   5 1         2     0      0       D
1805   9 0         3     1      0       I
1806   5 1         3     1      0       R
1808   3 1         1     1      0       D
1809   1 0         1     1      0       D
1810   3 1         4     0      0       R
1811   0 0         4     1      0       R
1812  10 1         0     0      0       R
1813   5 1         0     1      0       R
1814   0 1         0     1      0       D
1815   2 0         1     1      0       D
1816   8 1         1     1      0       D
1817   5 0         3     0      0       R
1819  10 1         5     1      0       R
1820   7 1         3     1      1       R
1821   2 0         3     1      0       I
1822   7 1         4     1      1       I
1823   5 1         3     1      0       D
1824   0 0         2     1      0       D
1825   5 0         3     1      1       D
1828   2 0         5     1      0       D
1829   0 1         0     0      0       D
1830   5 1         3     1      1       I
1831   1 0         1     0      1       D
1833   7 1         3     1      1       I
1834   4 1         5     0      0       D
1835   5 1         3     0      1       D
1837   9 1         3     0      1       I
1838   0 1         0     0      1       D
1840   5 1         3     1      1       R
1841   8 1         3     1      1       I
1842   2 1         3     1      1       I
1843  10 1         2     0      0       D
1844   5 0         4     1      0       R
1845  10 0         3     1      1       D
1846  10 1         3     1      1       I
1847   7 1         5     0      1       R
1848   5 1         3     1      0       D
1849   2 1         2     0      0       I
1850   6 1         1     0      0       D
1853   8 1         1     0      1       D
1856   1 1         3     0      1       D
1858   5 0         3     1      1       I
1859   1 1         2     1      1       R
1860   4 1         1     1      1       D
1861   6 1         2     0      1       D
1862   2 0         3     1      0       I
1864   9 1         4     0      1       D
1865   4 0         3     1      1       R
1866   1 0         2     0      1       D
1867   4 1         1     0      1       D
1868   0 1         4     1      1       R
1870   7 1         1     0      1       D
1871   5 1         3     1      1       I
1872   8 1         1     1      1       I
1874  10 1         5     1      0       R
1876   6 0         5     1      0       R
1877   2 1         5     1      1       R
1878   5 1         5     1      1       R
1880   5 1         1     1      1       D
1882   2 1         0     0      1       D
1883   2 0         3     1      1       I
1884   0 1         0     1      1       D
1886   6 1         4     1      0       D
1887   0 0         0     1      1       D
1888   4 1         3     1      0       I
1891   1 1         0     1      1       D
1892   3 1         1     0      1       D
1894  10 0         3     1      0       R
1895  10 0         5     1      1       R
1897   2 1         2     1      1       I
1900   5 1         5     1      1       R
1901   8 1         3     0      1       D
1902   3 1         1     1      0       D
1903   8 1         3     0      1       D
1906   3 1         1     0      1       I
1907   8 1         5     1      0       R
1908   3 0         1     0      1       D
1909   5 1         0     1      0       D
1910  10 0         3     0      0       D
1911  10 1         5     1      1       D
1913   6 1         0     0      1       D
1914   3 0         5     1      1       R
1915   0 1         1     1      1       I
1918   8 0         3     1      0       D
1919   7 1         3     0      0       D
1921   3 1         1     0      0       D
1922   1 1         5     0      0       R
1923   5 0         2     0      1       D
1924   2 1         3     1      1       D
1925   4 1         3     1      1       I
1926   9 1         0     0      1       D
1927   4 1         3     0      0       I
1928   0 1         2     1      1       I
1930  10 1         2     0      1       D
1931   8 0         3     1      0       R
1934   0 1         3     0      1       I
1935   4 0         3     1      1       I
1936   6 0         6     1      1       R
1937   2 1         3     1      0       R
1938   2 1         3     0      1       D
1939  10 1         0     1      0       R
1940  10 1         0     1      0       R
1941   5 0         0     0      1       I
1942   7 1         5     1      0       R
1943  10 1         0     1      0       R
1945   0 0         1     0      1       D
1946   9 1         2     0      0       D
1947   5 1         5     1      1       R
1948   3 1         3     1      1       D
1951   4 1         5     1      1       R
1952   9 1         1     0      1       I
1953   2 1         1     1      1       I
1954   2 1         5     1      1       R
1955   2 0         1     1      1       D
1956   4 1         3     1      1       I
1957   7 1         5     1      0       R
1958   6 0         3     0      0       D
1959   5 1         2     0      1       D
1960   3 1         4     0      0       I
1961   0 1         3     0      0       D
1962   7 1         1     0      1       D
1963   5 0         3     1      1       R
1964   5 1         5     1      1       I
1965   7 1         0     0      1       D
1966  10 1         4     1      0       R
1967   2 1         5     1      1       R
1968   6 1         5     1      1       R
1969   0 1         3     0      1       D
1973   0 1         6     1      1       R
1974   6 1         1     0      0       R
1977   9 1         5     1      0       R
1978   2 0         3     0      1       D
1979   4 0         3     0      1       I
1982   8 1         5     0      1       R
1983   3 1         4     0      0       D
1984   0 1         1     0      1       D
1990   4 1         3     1      1       D
1991   7 1         5     0      0       R
1992   0 1         3     1      0       I
1994   7 0         4     1      1       I
1995   3 1         3     0      1       D
1998   5 1         4     1      1       R
2000   2 1         3     1      1       I
2001   8 0         5     0      1       I
2002   5 1         2     0      1       I
2003   2 1         3     1      1       D
2004  10 1         3     1      0       D
2005   6 1         5     1      0       R
2006   6 1         5     1      1       R
2007   6 0         5     1      0       R
2008   4 1         0     1      1       I
2009   5 0         3     1      0       D
2010   1 1         0     0      0       D
2011   6 1         4     1      0       R
2012   7 0         0     0      0       D
2013   4 1         3     0      0       D
2014   5 1         1     0      1       D
2015   1 0         3     1      0       R
2016   4 0         3     1      1       R
2017  10 1         3     0      0       R
2018   7 1         5     1      1       R
2019   6 1         4     1      1       R
2020   0 1         5     1      0       R
2021   1 1         1     1      1       D
2022   1 1         4     1      1       R
2023   0 0         5     0      0       D
2024   8 1         1     1      1       I
2025   4 1         0     0      1       D
2026   5 1         3     1      0       D
2027   3 1         4     1      1       R
2028   0 0         3     0      1       D
2029  10 1         5     1      1       I
2030   5 0         2     0      1       D
2031   3 1         1     0      0       D
2032   3 0         4     1      1       I
2033  10 1         5     1      1       R
2034   1 1         5     1      0       R
2035   0 0         3     1      0       I
2037   0 1         6     1      0       R
2039   0 1         5     0      0       D
2040   2 0         5     1      0       R
2042   1 0         4     0      1       D
2043   5 1         3     0      0       I
2044   6 0         4     1      0       R
2045   3 1         6     1      1       R
2046   9 1         3     0      1       D
2048   6 0         0     1      0       I
2049   0 1         6     1      1       D
2050   3 1         5     0      0       D
2051  10 1         5     1      1       R
2052   2 0         5     1      1       R
2053   3 1         0     1      1       D
2054   4 1         1     1      0       D
2055   2 0         2     1      0       D
2056   7 1         2     1      1       I
2057  10 1         3     1      1       I
2058   2 1         3     1      1       R
2060   2 0         0     0      1       D
2061   2 1         3     0      1       I
2062   1 0         4     1      1       R
2063   1 1         3     1      1       I
2064  10 1         6     0      1       D
2065   8 1         3     1      0       R
2066  10 0         1     0      1       D
2067   0 1         0     1      1       D
2068   3 0         3     1      1       I
2069   1 1         5     1      1       R
2070   9 1         3     1      0       I
2071   4 1         1     1      1       I
2073   8 0         3     1      1       D
2075   1 1         1     1      1       D
2076  10 1         0     1      1       D
2077   3 0         2     1      1       D
2078   9 1         5     1      0       R
2079   5 0         3     0      1       D
2080   1 0         3     1      1       R
2081   4 0         1     1      1       I
2082   7 0         0     0      1       D
2083   5 0         3     0      1       D
2084   2 1         1     0      1       D
2085   5 1         2     1      1       R
2086   0 0         0     0      1       D
2087   5 0         3     0      0       I
2088   6 0         2     0      1       D
2089   0 1         1     0      1       D
2092  10 1         6     0      1       D
2093   5 1         6     0      0       D
2095   1 1         5     1      1       R
2098   3 0         3     0      1       R
2099   5 0         2     1      1       R
2100   2 1         3     0      1       I
2101   2 1         5     0      1       D
2102   9 0         0     0      0       D
2103   4 1         3     1      1       R
2104   5 1         1     0      0       D
2105   1 1         2     0      1       I
2107   0 0         5     0      0       R
2108   6 0         3     0      1       D
2109   0 0         2     1      1       D
2110   2 1         3     1      1       I
2111   0 1         3     0      1       I
2112   6 1         4     1      1       R
2113   2 1         3     1      0       R
2114   1 1         5     1      0       R
2115   9 1         3     1      0       R
2117   5 1         3     1      1       R
2118  10 1         1     1      0       R
2119   7 0         1     1      1       D
2120   7 1         6     1      1       R
2121   0 1         1     1      0       I
2122   0 0         0     0      1       D
2125   6 1         3     1      1       I
2126   8 1         3     1      1       I
2127   5 0         5     1      0       R
2129   6 1         3     0      1       D
2131  10 1         0     1      0       R
2132   0 0         0     1      1       D
2133   4 0         1     0      1       D
2134   8 1         5     1      0       I
2135   5 1         3     1      0       I
2136   5 1         3     1      1       D
2137   5 1         2     0      0       R
2138   7 0         6     1      1       R
2139   0 1         3     0      1       D
2140   7 1         5     1      1       R
2141   5 0         6     1      1       R
2142  10 1         3     0      1       D
2144   5 1         5     1      1       R
2145   8 1         5     1      0       R
2146   8 1         6     1      0       R
2147   6 0         0     0      1       D
2148   0 1         0     1      1       D
2149   0 1         5     1      1       R
2150   5 1         4     1      1       R
2151   4 1         3     1      1       R
2153   5 1         3     1      0       D
2154   7 0         0     0      0       D
2155   2 1         3     1      1       D
2156   8 1         4     1      0       R
2157  10 1         6     1      0       R
2158  10 1         4     1      1       I
2159   2 1         0     1      1       I
2160   2 1         0     0      0       D
2161   5 1         3     1      1       D
2162   5 1         3     1      1       D
2164  10 0         6     1      0       D
2165   1 1         2     1      1       D
2166   4 1         1     0      1       D
2167   5 1         4     0      0       D
2168   1 1         4     0      1       I
2169   0 0         0     1      1       D
2170   5 1         3     1      1       R
2171   4 1         5     0      0       D
2172   4 1         3     1      1       D
2173  10 1         1     1      1       R
2175   2 1         5     1      1       R
2176   8 1         5     1      0       R
2177  10 0         0     0      1       D
2178   9 1         0     1      0       R
2179   6 1         6     1      0       R
2181   9 1         5     1      0       R
2182   5 1         3     0      0       D
2183   6 0         3     1      1       I
2184   0 0         0     0      0       D
2186   8 1         4     1      1       R
2187   6 1         3     0      0       D
2188   8 1         3     1      1       I
2189   0 1         3     1      1       I
2190   7 0         3     1      1       I
2191   0 1         2     0      0       D
2192   3 0         5     1      0       D
2194   4 1         1     1      1       D
2195   0 0         3     0      1       D
2196   8 0         0     1      0       R
2197   2 1         3     1      0       R
2198  10 0         5     1      1       R
2199   8 1         2     1      0       R
2200   0 1         3     0      0       I
2201   4 1         3     0      1       R
2202   5 1         3     0      1       I
2203   9 0         1     0      0       D
2204   9 0         4     1      1       R
2205   5 1         1     1      0       I
2207   1 1         1     0      1       D
2208   3 1         3     0      1       I
2209   0 1         2     0      0       D
2210   2 1         1     0      1       I
2211   8 1         1     1      1       D
2212   0 1         0     0      1       D
2213  10 1         6     0      0       R
2214   3 1         3     0      1       D
2215   0 1         3     0      1       D
2216   2 1         6     0      0       I
2220   5 0         0     0      1       D
2221   6 1         2     0      0       D
2222   5 0         3     0      0       D
2223   2 0         2     0      0       I
2224  10 1         5     0      0       R
2225   3 1         4     1      1       R
2226   0 1         2     0      0       I
2227   5 1         1     0      1       D
2228   4 1         3     0      1       R
2229   4 0         4     0      0       D
2230   5 0         5     1      1       R
2233  10 0         3     1      0       R
2234   6 1         3     0      1       D
2235   5 0         1     1      1       D
2236   1 1         0     1      0       D
2237   5 1         3     1      1       I
2239  10 0         3     0      0       D
2240   6 1         2     1      0       I
2241   8 1         4     1      1       R
2242   5 1         3     1      1       I
2243   0 1         3     1      1       D
2245   4 1         3     0      1       D
2246   2 1         3     0      0       I
2247   5 1         4     1      1       D
2248   5 0         6     1      1       I
2249   5 0         1     1      1       D
2250   6 0         1     1      1       R
2251   3 1         4     1      1       R
2252   1 0         3     1      1       R
2254   5 1         3     1      1       I
2255   0 1         3     1      1       I
2256   5 0         3     1      1       I
2260   5 0         3     1      1       I
2261   2 0         3     1      0       I
2262   2 1         3     1      1       D
2263   1 1         2     1      1       D
2264   2 0         1     1      1       D
2265   5 1         1     1      0       D
2266   5 1         3     1      1       I
2267   5 1         3     1      0       R
2268   0 1         0     1      1       D
2269   8 1         3     1      1       R
2270   1 1         1     1      1       D
2271   2 0         0     1      1       D
2272   2 0         4     1      1       R
2273   2 1         1     1      0       D
2274   5 1         3     1      0       I
2275   2 0         4     1      0       R
2276   3 0         1     1      0       D
2277   0 1         0     1      0       D
2278   2 1         1     1      1       D
2279   0 1         2     1      1       R
2280   4 1         5     1      1       R
2281  10 1         3     1      1       D
2282   5 0         3     1      1       D
2283   3 0         6     1      1       R
2284   8 1         2     1      1       D
2285   6 1         3     1      1       I
2286   5 1         3     1      0       R
2287   1 1         0     1      1       I
2288   4 1         3     1      1       I
2289   1 0         1     1      1       D
2290   4 1         5     1      0       R
2291   5 1         3     1      1       D
2292   3 0         5     1      1       R
2293   5 1         5     1      1       I
2294   5 0         3     1      1       R
2295  10 1         0     1      1       I
2297   0 0         3     1      1       I
2298   0 0         2     1      1       I
2299   2 1         1     1      0       D
2300   6 1         5     1      0       I
2301   5 0         4     1      0       I
2302   2 1         3     1      0       I
2303  10 1         6     1      0       R
2305  10 0         3     1      1       I
2306   0 0         3     1      1       I
2307   4 1         3     1      0       I
2308   2 0         3     1      1       I
2309   7 0         3     1      0       D
2310  10 0         0     1      1       R
2311   4 1         3     1      0       I
2312   8 1         3     1      1       D
2313   6 0         5     1      0       D
2314   5 0         4     1      1       R
2315   0 0         1     1      1       D
2316   3 0         5     1      1       R
2317   0 0         0     1      1       D
2318   5 1         3     1      0       I
2319   5 1         5     1      1       I
2320   3 1         1     1      1       D
2321   8 1         6     1      1       I
2322   0 0         1     1      1       I
2323   9 1         1     1      0       D
2324   2 1         3     1      1       R
2325   5 1         6     1      1       R
2326   7 1         5     1      1       R
2327   1 1         6     1      1       R
2328   2 1         0     1      1       R
2329   4 1         3     1      1       R
2330   0 0         0     1      1       D
2331  10 1         1     1      1       D
2332   1 0         3     1      0       I
2333   6 1         5     1      0       R
2334   3 0         3     1      1       D
2335   2 1         3     1      1       I
2336   8 1         1     1      0       D
2337   4 1         2     1      1       D
2338   4 1         0     1      0       D
2339   5 1         1     1      1       I
2340   4 1         3     1      0       D
2342   5 1         3     0      0       I
2343   1 0         1     1      0       D
2345   1 1         2     1      1       I
2346   9 0         3     1      1       D
2347   3 1         5     1      0       R
2348   7 1         3     1      1       R
2350   1 1         3     1      1       D
2351   4 1         3     1      0       R
2352  10 1         0     1      0       R
2353   5 1         3     1      0       D
2354   6 1         0     1      0       I
2355   7 0         3     1      0       I
2356   8 1         0     1      0       D
2357  10 1         5     1      0       D
2358   1 1         6     1      0       I
2359   2 1         1     1      0       D
2360   4 0         4     1      0       I
2362   6 0         3     1      0       D
2363   9 1         5     1      0       R
2364   7 1         3     1      0       R
2366   2 1         1     1      0       I
2367   7 1         3     1      0       I
2370   7 1         1     1      0       R
2371   6 1         2     1      0       I
2372   1 0         2     1      0       I
2373   5 1         5     1      0       D
2374   5 1         5     1      0       R
2375   5 1         2     1      0       I
2376   6 1         5     1      0       R
2378   8 0         5     1      0       R
2379  10 1         4     1      0       R
2380   7 1         2     1      0       D
2381   2 1         5     1      0       R
2382   6 1         5     1      0       R
2383   6 1         3     1      0       D
2385   8 1         4     1      0       R
2386   0 1         3     1      0       I
2387   6 1         5     1      0       I
2388   0 1         6     0      0       I
2389   5 0         3     1      0       I
2390   4 0         4     1      0       R
2391   7 0         3     1      0       D
2393   0 1         0     1      0       D
2395   0 0         0     1      0       D
2396   6 0         3     1      0       I
2397  10 0         3     1      0       I
2398   5 1         1     1      0       I
2399   3 1         5     1      0       R
2400  10 0         3     1      0       I
2401   7 1         5     1      0       D
2402   4 1         1     1      0       I
2403   5 0         5     1      0       R
2405   2 0         3     1      0       I
2406  10 0         3     1      0       D
2407   4 1         2     1      0       D
2408   7 0         0     1      0       D
2409   3 0         3     1      0       D
2410   2 1         5     1      0       I
2412   5 0         3     1      0       R
2413   7 0         3     1      0       D
2414   6 1         5     1      0       R
2415   5 1         1     1      0       D
2416   0 1         3     1      0       I
2417   6 1         3     1      0       I
2419  10 1         6     1      0       R
2420   1 1         3     1      0       I
2421   6 1         1     1      0       I
2425  10 1         3     1      0       R
2426   8 1         3     1      0       D
2428   5 0         3     1      0       I
2429  10 1         1     1      0       I
2430   5 1         0     0      0       R
2431   1 0         4     1      0       I
2433   3 0         1     1      0       I
2434  10 1         5     1      0       R
2435  10 1         5     1      0       R
2436   1 0         2     1      0       I
2440   6 0         3     1      0       I
2441   6 1         0     1      0       D
2442   5 1         3     1      0       R
2443   9 1         6     1      0       R
2444   7 0         2     1      0       I
2446   5 0         1     1      0       D
2448   5 1         5     1      0       R
2449   6 1         3     1      0       I
2450   0 0         3     0      0       D
2452   3 1         3     1      0       D
2455   8 1         5     1      0       R
2457   5 1         3     1      0       D
2458   2 1         3     1      0       I
2459   7 0         4     1      0       D
2460   1 0         3     1      0       I
2463   9 1         3     1      0       R
2466   7 1         5     1      0       I
2467   0 0         3     1      0       R
2468   3 1         1     1      0       R
2469   2 1         1     1      0       I
2470   5 0         3     1      0       I
2471   1 1         6     1      0       R
2472   7 1         3     1      0       I
2473   5 1         3     1      0       R
2474   3 0         4     1      0       R
2475   8 1         3     1      0       I
2477   3 1         4     0      0       R
2480   0 0         2     1      0       D
2482   2 0         4     1      0       R
2486   8 0         3     1      0       I
2487   0 1         0     1      0       I
2488   6 0         1     1      0       D
2489   5 0         3     1      0       I
2490   0 1         5     1      0       D
2491   3 0         3     1      0       I
2493   1 0         3     1      0       D
2494   5 1         3     1      0       I
2495   4 1         5     1      0       D
2496   5 0         3     1      0       I
2497   3 1         3     1      0       I
2499   8 1         5     1      0       I
2500   3 1         3     1      0       R
2503  10 0         0     1      0       D
2504   0 1         0     1      0       D
2506   6 1         6     1      0       R
2507   6 1         3     1      0       I
2508   3 0         1     1      0       D
2509   4 0         0     1      0       D
2511   0 0         3     1      0       D
2512   3 1         5     1      0       I
2514   5 0         1     1      0       D
2516   4 0         3     1      0       I
2517   6 1         3     1      0       R
2518   2 1         4     1      0       R
2519   5 1         1     1      0       D
2520   6 0         3     1      0       I
2521   4 1         4     1      0       D
2523   1 1         1     1      0       D
2524  10 1         3     1      0       R
2525  10 1         5     1      0       D
2526   0 1         3     1      0       I
2527   2 1         1     1      0       D
2528   0 1         2     1      0       D
2529   1 1         1     1      0       D
2530   0 1         1     1      0       D
2532   5 1         3     1      0       R
2533   5 1         3     1      0       I
2534   3 0         4     1      0       I
2535   1 1         3     1      0       D
2536   1 1         0     1      0       D
2537  10 1         4     1      0       R
2539   1 1         1     1      0       I
2540   7 1         3     1      0       I
2541   8 1         3     1      0       I
2542   3 0         5     1      0       R
2543   6 0         5     1      0       R
2544   2 0         3     1      0       I
2545   2 0         3     1      0       I
2546   3 0         1     1      0       D
2547   2 1         6     1      0       R
2548   0 1         3     1      0       I
2549   3 0         5     1      0       R
2550   0 1         3     1      0       R
2551   6 1         3     1      0       I
2552   5 1         5     1      0       R
2554   1 1         3     1      0       I
2555   5 1         3     1      0       I
2556   6 1         3     1      0       R
3100   9 0         4     1      1       R
4100  10 0         3     1      1       R
5100   2 0         1     1      1       D
6100   5 0         5     1      0       I
7100   3 0         5     1      0       R
8100   8 0         3     1      1       I
9100   0 0         1     1      0       D
10100  9 0         5     1      0       R
11100  1 0         3     1      1       D
12100  0 0         4     1      0       I
13100  8 0         5     1      1       R
14100  3 0         5     1      0       R
15100 10 0         6     1      0       D
16100  2 0         4     1      1       R
17100  1 0         3     0      1       D
18100  6 0         1     1      1       D
19100  0 0         5     1      1       R
20100  2 0         3     0      1       I
21100  7 0         3     1      1       I
23100  4 0         3     1      0       R
24100  7 0         5     1      1       R
2557   2 0         3     1      1       R
2610   4 0         2     0      1       D
2710   7 0         1     1      0       R
2810   2 0         2     1      0       D
3010   8 0         3     1      0       R
3110   5 0         5     1      0       R
3210   9 0         4     1      1       I
3310   5 0         0     1      0       R
3510   9 0         3     1      0       D
3610  10 0         0     0      0       R
3710   0 0         3     0      1       D
3910   1 0         2     0      1       D
4310   8 0         1     0      1       R
4410   3 0         2     0      1       D
4610   9 0         2     0      0       D
4710   5 0         3     1      1       R
4810  10 0         1     0      0       D
4910   6 0         3     1      0       R
5010   3 0         5     1      0       R
5110   7 0         2     1      0       D
5210   0 0         3     0      0       I
5310   1 0         1     0      0       I
5410   7 0         2     1      0       D
5510   4 0         5     1      0       R
5810   5 0         2     0      1       R
5910   9 0         3     1      0       R
6110   6 0         3     1      1       D
6210   4 0         3     0      1       D
6310   9 0         0     0      1       I
6410   7 0         1     0      1       I
6610   5 0         3     1      1       I
6810   4 0         4     0      0       I
6910   1 0         3     1      1       I
7210   8 0         4     0      1       I
7310   8 0         2     0      1       I
7410   4 0         3     1      1       D
7610   6 0         3     0      1       D
7710   0 0         1     0      1       D
7810   0 0         1     1      1       I
7910   0 0         0     1      1       D
8310  10 0         5     0      0       D
8510   3 0         5     1      1       R
8610   1 0         0     0      0       I
8710   4 0         1     0      0       D
8810   2 0         6     1      1       R
8910   2 0         6     1      0       R
9010   7 0         4     0      1       I
9110  10 0         3     0      1       D
9210   6 0         0     0      0       D
9310   3 0         1     1      1       D
9410   2 0         4     1      0       R
9610  10 0         6     1      1       R
10010  3 0         3     0      1       I
10110  4 0         1     1      1       D
10510  1 0         6     1      1       R
10610  7 0         5     1      0       R
10810 10 0         2     0      1       D
11010  2 0         1     1      1       D
11110  2 0         1     0      1       D
11310  5 0         3     0      1       R
11410  7 0         0     0      1       D
11510  0 0         3     1      0       D
11610  9 0         5     1      1       R
11710  8 0         3     0      1       D
11810  5 0         5     1      0       R
11910  4 0         3     0      1       D
12010  3 0         5     1      1       R
12310  8 0         3     1      0       R
12410  2 0         1     1      1       D
12510  7 0         1     1      0       R
12610  4 0         4     0      1       D
12710  6 0         2     1      1       D
12810  6 0         5     1      1       R
13110  5 0         1     1      1       R
13210  1 0         3     1      1       D
13310  7 0         3     0      1       I
13410  8 0         5     0      0       R
13510  5 0         4     1      1       I
13610  6 0         1     1      0       I
13810  1 0         4     1      0       R
13910  2 0         0     0      1       D
14110  8 0         3     1      1       I
14210  0 0         3     1      1       I
14310  5 0         3     0      0       D
14410  2 0         3     1      1       I
14510  5 0         6     1      1       R
14610  5 0         4     1      1       D
14710  4 0         4     1      0       D
14910  2 0         3     1      1       R
15010  6 0         3     0      0       I
15110  1 0         1     1      1       D
15210  2 0         0     0      0       D
15310  0 0         1     1      1       D
15610  1 0         5     1      1       R
15910  3 0         3     1      1       R
16110  3 0         3     0      1       I
16210  9 0         3     1      1       I
16410 10 0         2     0      0       D
16510  9 0         3     1      1       D
16610 10 0         1     1      1       D
16710  2 0         4     1      1       R
16810  1 0         1     0      1       D
16910 10 0         1     1      0       R
17010  1 0         4     1      1       D
17110  0 0         3     0      0       I
17210  1 0         4     1      0       R
17310  3 0         3     1      0       I
17410  4 0         1     1      1       D
17510  2 0         5     1      1       R
17610  9 0         5     1      1       R
17710  5 0         0     1      1       D
17810  2 0         1     1      1       D
17910  5 0         6     1      0       R
18010  2 0         3     1      1       I
18210  8 0         5     1      1       R
18310  3 0         3     1      0       R
18410 10 0         3     1      1       D
18510  2 0         3     0      1       I
18610  0 0         5     1      0       I
18710  9 0         3     1      1       R
18810  1 0         0     1      1       D
18910  8 0         5     1      0       R
19010  4 0         3     1      0       D
19110  1 0         3     1      1       D
19210  5 0         3     1      1       I
19310  0 0         3     1      0       I
19410  8 0         3     1      1       D
19510  1 0         2     1      1       D
19610  2 0         4     1      1       I
19710  2 0         4     1      1       R
19810  3 0         5     1      1       D
19910  7 0         0     0      1       D
20110  2 0         1     1      0       D
20210  7 0         3     0      0       I
20310  4 0         1     1      1       D
20410  0 0         5     1      1       R
20510  0 0         3     0      1       D
20610  1 0         6     1      1       R
20710  1 0         5     1      0       R
20810  6 0         5     1      0       R
20910  7 0         4     1      1       R
21010  1 0         1     1      1       D
21110  0 0         1     0      1       D
21210  4 0         3     0      0       D
21310  2 0         3     0      1       D
21410  5 0         3     1      1       I
21510  1 0         1     1      1       D
21610  4 0         3     1      1       I
21710  5 0         5     1      1       R
21810  1 0         5     1      1       R
21910  0 0         5     1      1       R
22010  4 0         3     1      1       R
22110 10 0         6     1      1       I
22210  9 0         0     1      1       D
22310  5 0         5     1      1       I
22410  7 0         3     1      1       D
22510 10 0         6     1      1       R
22710  5 0         3     1      1       D
22810  6 0         5     1      0       I
23010  1 0         1     1      1       D
23110  5 0         0     1      1       D
23210  4 0         3     0      0       D
23310  8 0         3     1      1       R
23410  5 0         4     0      1       I
23510  2 0         1     0      1       D
23610  5 0         2     0      1       D
23710  6 0         5     1      1       R
23810  5 0         4     1      1       D
23910  2 0         3     1      1       R
24010  0 0         2     1      1       D
24110  2 0         4     1      1       R
24210  4 0         5     1      1       R
24310  0 0         1     1      0       D
24410 10 0         5     1      1       R
24510  0 0         0     1      1       I
24610 10 0         3     1      0       I
24710  3 0         5     1      1       R
24810  4 0         3     1      1       D
24910  0 0         5     1      1       R
25010  7 0         5     0      1       R
25110  1 0         6     1      0       R
25210  3 0         3     1      1       I
25310  1 0         3     0      1       D
25410  0 0         2     1      1       D
2558   5 0         5     1      0       R
2561   4 0         4     1      0       D
2571   1 0         1     1      1       D
2581   0 0         3     1      1       D
2591   4 0         1     0      1       R
2601   1 0         3     1      1       D
2621   0 0         3     1      1       I
2631   2 0         3     1      1       D
2641   9 0         6     1      0       I
2651   4 0         2     1      1       I
2661   0 0         0     1      1       D
2671   4 0         4     1      1       R
2681   7 0         6     1      1       R
2691   0 0         3     1      0       D
2701   1 0         4     1      0       R
2711   6 0         3     1      1       D
2721   8 0         3     1      1       D
2731   7 0         3     1      1       R
2751   5 0         3     0      1       D
2761   6 0         5     1      0       R
2771   2 0         3     1      1       D
2781   1 0         4     1      1       I
2791   5 0         3     0      0       D
2801   1 0         4     1      0       R
2811   1 0         3     0      1       D
2821  10 0         5     0      0       I
2831   4 0         3     1      1       I
2841   2 0         3     1      1       I
2851   2 0         2     1      1       D
2861   5 0         3     1      1       D
2871   4 0         5     1      0       R
2881   0 0         2     1      1       I
2891   4 0         1     1      1       D
2901   4 0         6     1      0       R
2911   5 0         3     1      1       I
2921   9 0         3     1      1       I
2931   0 0         3     1      1       R
2941   0 0         3     0      1       D
2951   2 0         3     1      1       D
2971   1 0         1     1      1       D
2981   5 0         6     1      1       R
2991   2 0         0     1      1       D
3001   1 0         1     1      0       D
3011   6 0         5     1      0       R
3021   7 0         4     1      0       R
3031   5 0         4     1      1       I
3041   1 0         1     1      1       D
3051   1 0         3     0      1       D
3061   0 0         1     1      0       D
3071   3 0         6     1      0       R
3081   5 0         2     1      0       D
3091   0 0         0     1      1       D
3101   8 0         1     1      1       D
3111  10 0         1     0      1       D
3121   5 0         1     1      0       D
3131   7 0         3     1      0       R
3141  10 0         5     1      1       R
3151   2 0         6     1      0       R
3171   0 0         1     1      0       D
3181   8 0         6     1      1       R
3191   3 0         6     1      0       R
3211   1 0         3     0      0       D
3221   1 0         1     0      1       D
3231   1 0         5     1      1       R
3241   0 0         1     1      1       D
3251   3 0         3     0      0       D
3261   8 0         4     1      0       I
3271   0 0         1     0      1       D
3281   1 0         1     1      1       D
3291   1 0         2     1      0       D
3301   2 0         3     0      1       D
3311   3 0         3     1      0       D
3321   3 0         2     1      0       R
3331  10 0         1     0      1       D
3341   8 0         1     1      0       R
3351   6 0         6     1      1       I
3361   5 0         3     1      1       I
3371  10 0         6     1      1       R
3381   0 0         6     1      1       R
3391   5 0         3     1      1       D
3401  10 0         3     1      1       D
3411   7 0         3     1      1       D
3421  10 0         5     1      1       R
3451   6 0         6     1      0       R
3461   3 0         1     0      0       D
3471   1 0         2     1      0       D
3491   0 0         4     1      1       I
3501   0 0         3     0      1       D
3511   1 0         5     1      1       I
3521   4 0         3     1      1       I
3531   5 0         1     0      0       D
3541   0 0         3     1      1       D
3551   2 0         1     1      0       I
3561   2 0         2     1      0       I
3571   0 0         3     0      1       I
3581  10 0         4     1      0       R
3591   3 0         3     0      0       D
3601  10 0         5     0      0       R
3611   9 0         3     0      1       D
3621   5 0         1     1      1       D
3631   8 0         0     1      0       D
3641   3 0         2     1      1       D
3651   4 0         6     1      1       R
3661   9 0         2     1      1       I
3681   5 0         4     1      0       R
3691   1 0         3     1      0       D
3701   5 0         5     1      1       R
3711   0 0         3     1      0       I
3721   0 0         0     1      1       I
3731   1 0         1     1      1       D
3741   0 0         3     0      0       D
3751  10 0         4     1      1       R
3761   0 0         0     0      0       D
3771  10 0         4     1      0       I
3781   3 0         5     1      1       R
3791  10 0         5     1      0       D
3801  10 0         1     0      0       R
3811   7 0         3     1      0       I
3821   8 0         3     0      0       I
3831   6 0         3     1      1       I
3841   1 0         0     1      0       D
3851  10 0         1     1      0       R
3861   1 0         1     1      0       I
3871  10 0         6     1      0       R
3881   6 0         5     1      1       R
3901   0 0         5     1      1       R
4021   2 0         5     1      1       R
4031   2 0         0     0      1       D
4061   2 0         5     1      0       R
4081   3 0         1     1      1       D
4101   0 0         4     1      1       R
4131   3 0         6     1      1       R
4141   0 0         6     1      0       R
4161   1 0         1     1      1       D
4171  10 0         6     0      0       R
4181  10 0         4     1      0       R
4191   3 0         0     1      1       D
4201   0 0         4     1      0       I
4221   0 0         1     1      1       D
4241   3 0         4     1      1       R
4251   0 0         5     1      0       R
4261   2 0         1     0      0       D
4281   4 0         5     1      1       R
4301   1 0         3     1      1       D
4311   0 0         1     1      0       D
4391   3 0         3     1      0       D
4401   3 0         3     1      0       R
4411   0 0         1     1      1       D
4451   2 0         6     0      0       D
4461   9 0         3     1      0       I
4511   3 0         0     0      0       I
4521   0 0         1     1      1       D
4531   0 0         3     1      0       I
4541   3 0         1     1      1       D
4561   6 0         3     1      0       I
4571   5 0         6     1      0       R
4581   6 0         1     1      0       D
4591   3 0         3     1      0       R
4621   8 0         3     1      1       R
4651   3 0         1     0      1       D
4661   0 0         3     1      1       I
4691   0 0         4     1      1       I
4711   2 0         5     1      1       R
4721   0 0         1     0      1       D
4731   5 0         3     1      1       I
4771  10 0         3     1      1       D
4781   7 0         5     1      0       R
4981   5 0         3     0      0       D
5011   5 0         5     1      1       R
5061   3 0         1     0      0       D
5081   8 0         1     0      0       D
5141   2 0         3     0      0       I
5191   9 0         6     1      0       D
5381   4 0         4     0      1       R
5391   6 0         3     1      0       R
5411   1 0         3     1      1       I
5451   7 0         1     0      1       D
5511   0 0         3     1      1       I
5531   9 0         1     0      1       D
5541   9 0         0     0      0       R
5551   2 0         6     1      1       I
5601  10 0         6     1      1       D
5611   5 0         3     0      0       D
5621   5 0         1     0      0       R
5631   5 0         3     0      0       D
5641   0 0         0     0      0       D
5651   5 0         3     0      0       I
5661   2 0         5     0      0       I
5701   3 0         6     1      1       I
5771   8 0         2     1      1       I
5791   5 0         3     1      1       I
5801   8 0         1     1      0       I
5811   2 0         3     1      1       I
5831   7 0         3     1      1       I
5851   7 0         3     1      1       D
5861   5 0         5     0      1       D
5891   0 0         1     0      1       D
5911   6 0         3     1      1       I
5921   3 0         3     1      1       I
5931   7 0         1     0      1       D
5961   7 0         5     1      1       R
5971   2 0         1     0      1       I
5981  10 0         2     1      1       D
5991   6 0         2     1      0       I
6001   7 0         1     0      0       R
6011   2 0         1     0      0       D
6021   4 0         1     0      1       R
6031   3 0         2     1      0       D
6041   5 0         3     1      1       R
6051   5 0         3     0      1       D
6061   0 0         0     1      1       D
6071   8 0         3     0      0       I
6081   0 0         3     1      1       I
6101   7 0         3     1      0       D
6111   7 0         5     1      1       R
6121  10 0         6     1      1       R
6131   0 0         3     1      0       I
6141   4 0         3     0      1       D
6151  10 0         1     1      0       D
6161   5 0         3     1      1       R
6181   5 0         3     1      1       I
6201   0 0         0     1      0       D
6211   0 0         0     0      1       D
6221   4 0         0     1      1       D
6231   5 0         1     0      0       I
6241  10 0         3     0      1       I
6251   9 0         3     0      1       I
6281   6 0         3     0      0       D
6291   5 0         1     0      1       D
6301  10 0         3     0      0       I
6311   0 0         0     0      0       R
6321   2 0         3     0      0       R
6341   9 0         0     0      0       D
6361   7 0         3     1      1       D
6371   3 0         2     0      1       D
6381   0 0         0     0      1       D
6391   4 0         4     0      1       D
6401   7 0         3     0      1       D
6411  10 0         2     1      0       R
6421   4 0         1     0      0       D
6431   7 0         1     0      1       D
6441   8 0         1     1      0       D
6451   0 0         1     0      0       I
6461   8 0         5     0      1       R
6471   6 0         2     1      1       R
6491  10 0         0     0      0       D
6501   1 0         3     0      1       I
6511   7 0         5     0      1       I
6521   3 0         3     0      1       D
6541   6 0         2     1      0       D
6561   3 0         3     0      0       I
6571   0 0         1     0      0       R
6581   5 0         2     0      0       D
6591   5 0         3     0      0       D
6611   9 0         6     1      0       R
6621   4 0         3     1      0       I
6631   2 0         3     0      0       I
6651   7 0         3     0      0       R
6661   8 0         4     1      1       I
6671   5 0         3     1      0       D
6681   9 0         1     0      0       R
6691   4 0         5     0      0       R
6701   5 0         3     0      0       I
6721   7 0         4     1      0       R
6751   3 0         3     0      1       D
6761  10 0         3     0      0       I
6771   7 0         1     0      0       R
6791   1 0         4     0      0       D
6801   2 0         6     1      0       R
6811   5 0         3     0      1       I
6851   4 0         3     1      0       D
6861   5 0         5     0      0       I
6871   0 0         5     0      0       I
6891   0 0         3     0      0       D
6901   8 0         0     0      0       R
6921   2 0         5     1      0       I
6931   0 0         3     0      0       I
6951   2 0         3     0      0       D
6961   0 0         3     0      0       D
6971   8 0         4     0      0       R
6981   5 0         3     0      0       I
7001   4 0         2     0      0       D
7011  10 0         5     1      0       R
7031   0 0         1     0      0       D
7041   6 0         4     0      0       R
7051   4 0         1     0      0       D
7061   8 0         0     1      0       D
7071   0 0         0     0      0       I
7091   6 0         5     0      0       I
7101   3 0         4     0      0       R
7111   5 0         1     0      0       D
7121   9 0         2     0      0       D
7141   9 0         0     1      0       D
7151   0 0         3     0      0       R
7161   1 0         1     0      0       D
7171   1 0         1     0      0       D
7191   3 0         3     0      0       D
7211   9 0         0     0      0       D
7231   3 0         3     0      0       R
7271   0 0         4     1      0       R
7321   9 0         5     0      1       D
7331   5 0         3     0      0       D
7461   0 0         4     1      0       R
7471   1 0         3     1      0       I
7481   7 0         1     0      0       I
7491   5 0         5     1      0       R
7501   0 0         1     0      0       D
7511   8 0         3     0      0       D
7531   6 0         2     1      0       I
7541   0 0         3     1      0       I
7551   1 0         3     1      0       I
7561   7 0         4     0      0       R
7591   3 0         4     0      1       D
7601   7 0         3     1      0       D
7611   7 0         0     0      0       D
7621   0 0         0     0      0       D
7651   4 0         3     0      0       I
7671   2 0         1     1      1       D
7681   2 0         2     0      0       D
7691   7 0         3     0      0       D
7711   0 0         2     0      0       I
7721   3 0         1     0      0       D
7731   5 0         0     0      0       I
7741   4 0         3     0      0       I
7751   5 0         2     0      0       D
7781   5 0         5     1      0       R
7801   3 0         1     0      0       D
7831   8 0         0     0      0       R
7861   7 0         4     0      1       I
7871   2 0         1     0      1       D
7881   6 0         1     1      0       D
7891   5 0         1     0      0       I
7901   8 0         5     1      0       R
7911   1 0         2     0      1       I
7921   0 0         0     0      0       D
7931  10 0         1     1      0       R
7941   9 0         6     0      0       D
7951   8 0         5     1      0       R
7971   4 0         4     0      1       I
8001   0 0         3     0      1       D
8011   3 0         2     0      0       D
8021  10 0         5     0      0       R
8031   0 0         1     0      1       I
8041   2 0         3     0      1       I
8051   0 0         1     1      1       D
8061   4 0         1     0      1       D
8071   3 0         4     1      0       I
8081   0 0         3     0      0       D
8111   0 0         3     0      1       R
8121   4 0         3     0      1       D
8131   0 0         0     0      1       D
8151   3 0         4     0      1       D
8161   7 0         6     0      0       R
8201   3 0         0     0      1       D
8231   5 0         4     1      1       D
8251   6 0         1     0      0       I
8271   0 0         2     0      1       D
8281   9 0         4     0      1       D
8311   8 0         3     1      1       D
8321   4 0         3     1      1       I
8341   6 0         3     1      0       R
8351   4 0         3     1      0       I
8381   7 0         0     1      0       R
8391   5 0         3     0      1       I
8401   0 0         0     1      1       I
8461  10 0         0     1      0       D
8481   3 0         4     1      1       R
8491   9 0         3     1      0       R
8521  10 0         0     1      0       R
8541   4 0         6     1      0       R
8551   0 0         1     1      1       D
8571  10 0         5     1      0       R
8581   3 0         2     1      1       R
8591   1 0         3     1      1       R
8601  10 0         3     1      0       D
8611   6 0         3     1      1       D
8621   4 0         2     1      0       D
8631   8 0         1     1      0       D
8641   8 0         5     1      1       R
8661   0 0         3     1      1       D
8681   0 0         3     1      1       D
8701   0 0         0     1      1       D
8711   6 0         3     1      0       I
8731   3 0         3     1      1       R
8771   8 0         5     1      0       R
8781   5 0         4     1      0       R
8791   6 0         1     0      1       D
8801   3 0         1     1      1       R
8811   1 0         4     1      0       R
8861   7 0         4     1      1       R
8901   5 0         4     1      1       R
8931   2 0         2     1      0       R
8951   0 0         0     1      0       I
8961   6 0         1     1      0       D
8971   6 0         5     1      0       R
8981   5 0         5     1      0       R
8991   5 0         1     1      0       R
9001  10 0         3     1      0       R
9011   1 0         2     1      0       I
9021   7 0         0     1      0       I
9041   5 0         3     1      0       I
9071  10 0         3     1      0       R
9131   5 0         0     1      0       I
9151   7 0         3     0      0       D
9161   9 0         5     1      0       R
9201  10 0         1     0      0       D
9211   3 0         3     1      0       R
9221   6 0         1     1      0       I
9251   7 0         5     0      0       R
9271   0 0         1     1      0       R
9281   5 0         2     1      0       I
9291   4 0         3     1      0       I
9301   8 0         2     1      0       R
9311   0 0         4     1      0       I
9331  10 0         0     1      0       R
9341   7 0         0     1      0       R
9361   7 0         4     1      0       D
9381   8 0         3     1      0       I
9481   7 0         3     1      0       D
9491   2 0         1     0      0       I
9511   9 0         6     1      0       D
9561   4 0         3     1      0       R
9621   6 0         4     1      0       I
9681   5 0         3     1      0       R
9701   4 0         3     1      0       D
9741   0 0         0     1      0       D
9751   8 0         1     1      0       R
9761   1 0         4     1      0       I
9771   0 0         3     1      0       R
9791   2 0         0     1      0       D
9861   9 0         6     1      0       D
9871   1 0         1     0      1       D
9891   0 0         3     1      1       R
9921   0 0         6     1      1       R
9951   5 0         4     1      0       R
9961   7 0         3     1      1       I
9991   4 0         3     1      1       D
10001 10 0         6     1      1       R
10021  1 0         3     1      1       R
10041  5 0         4     1      0       R
10051  0 0         1     1      1       I
10071  2 0         3     1      0       I
10091  1 0         1     1      1       D
10111  5 0         6     1      0       R
10121  2 0         3     1      0       I
10141  0 0         3     1      1       R
10151  7 0         1     1      0       D
10161  8 0         2     1      0       D
10171  9 0         5     1      0       R
10181  4 0         3     1      0       I
10191  4 0         4     1      0       R
10201  0 0         1     0      1       D
10211  6 0         4     1      0       D
10231  5 0         3     1      1       I
10241  2 0         1     1      0       D
10281  4 0         4     1      0       R
10311  5 0         3     1      1       I
10321  4 0         4     1      1       D
10381  3 0         2     0      1       D
10401  7 0         4     0      0       I
10421  8 0         3     1      0       D
10441  3 0         3     1      1       D
10451  8 0         5     1      1       R
10491  0 0         3     1      1       D
10501  6 0         4     1      1       R
10511  6 0         3     1      1       D
10521  5 0         5     1      0       R
10531  5 0         3     1      1       I
10541  5 0         3     0      1       D
10561  5 0         3     1      1       R
10571  6 0         3     1      1       R
10581 10 0         5     1      1       R
10591  4 0         3     1      1       R
10611  7 0         3     0      0       D
10631  5 0         6     1      1       R
10641  5 0         5     1      0       I
10661  9 0         1     1      1       I
10671 10 0         3     1      1       I
10681  2 0         1     0      1       I
10701  1 0         0     1      0       D
10711  4 0         4     0      0       D
10721  0 0         5     1      1       I
10731  4 0         5     1      1       R
10741  5 0         4     1      0       I
10751  7 0         2     1      1       D
10761  7 0         1     1      1       D
10821  1 0         2     1      1       D
10871  2 0         1     1      1       D
10891  7 0         1     1      0       D
10911  5 0         3     1      1       I
10921  5 0         6     1      1       R
10941  5 0         4     1      1       R
10991  3 0         1     1      1       D
11001  0 0         3     1      1       D
11021  5 0         2     1      1       D
11071  7 0         5     1      0       R
11081  0 0         2     1      1       I
11091  0 0         2     1      1       D
11101  0 0         6     1      1       R
11111  5 0         3     1      1       D
11121  0 0         6     1      1       R
11151  1 0         6     1      0       R
11161  2 0         1     1      0       I
11171  3 0         5     1      1       R
11181  0 0         1     1      0       D
11201  5 0         1     1      0       D
11211  7 0         4     0      1       I
11221  6 0         3     1      1       I
11231  6 0         1     1      0       R
11241  1 0         2     1      1       I
11251  3 0         3     1      1       I
11261  0 0         4     1      1       D
11291  0 0         3     1      0       I
11301  0 0         4     1      0       I
11321  5 0         3     1      1       I
11521  6 0         2     1      0       R
11541  2 0         3     1      1       D
11561  5 0         4     1      0       R
11571  5 0         1     1      1       I
11581  7 0         3     1      1       I
11591  0 0         5     1      1       R
11611  2 0         5     1      1       R
11621  3 0         3     1      1       I
11641  0 0         5     1      0       R
11651 10 0         1     1      0       R
11661 10 0         5     1      0       I
11691  1 0         5     1      0       R
11721 10 0         3     1      0       R
11751  9 0         5     1      0       R
11761  4 0         0     1      0       D
11861  2 0         0     1      0       D
11871  5 0         6     1      0       I
11881  2 0         1     1      0       D
11891  6 0         3     1      0       D
11901 10 0         0     1      0       R

Results

main1 = difference_in_means(Y ~ Z, data = w2) %>% tidy()

main2 = lm_robust(Y ~ Z, data = w2) %>% tidy()

adj = lm_robust(Y ~ Z + white + female + partyID, data = w2) %>% tidy()

estimator	estimate	std.error	conf.low	conf.high	p.value
Diff. in means	0.476	0.119	0.242	0.709	0.0000662
OLS (no controls)	0.476	0.119	0.242	0.709	0.0000662
OLS + controls	0.413	0.116	0.185	0.642	0.000392

What if I don’t have random assignment?

Strategy 2: Ignorability

What if we cannot assume random assignment?

Strategy 2: Ignorability

We can still conduct valid causal inference if we believe treatment assignment is strongly ignorable (conditional on covariates)

Requirements:

• Conditional independence: \((Y_i(0), Y_i(1)) \perp \!\!\! \perp D_i | \mathbf{X}_i\)
• Positivity: There exists \(\epsilon > 0\) such that \[\epsilon < Pr[D_i = 1 | \mathbf{X}_i] < 1 - \epsilon\]

Weak ignorability only requires \(Y_i(d) \perp \!\!\! \perp D_i | \mathbf{X}_i \forall d \in \{0, 1\}\), which in most cases makes no difference

Strategy 2: Ignorability

If strong ignorability holds:

• ATE \(E[\tau_i]\) is point-identified
• Conditional ATE (CATE) \(E[\tau_i | \mathbf{X}_i]\) is point-identified

Estimation strategies (more in the lab):

• Conditioning on covariates (regression)
• Propensity score matching
• IPW estimation
• Doubly robust estimation

Post-treatment variables

Randomization implies independence: \((Y_i(0), Y_i(1)) \perp \!\!\! \perp D_i\)

Strong ignorability requires conditional independence: \((Y_i(0), Y_i(1)) \perp \!\!\! \perp D_i | \mathbf{X}_i\)

Neither needs to be true for post-treatment variables

Conditioning on post-treatment variables introduces bias

See Montgomery, Nyhan, and Torres (2018) for details

Wrapping up

• Causal inference requires imposing additional assumptions

• Easy to justify with experiments (but hard to implement)

• Hard to justify in observational studies (easy to p-hack, HARK)

• Next step: “Quasi”-experimental designs

Bonus: Quasi-experiments

What if we could guarantee strong ignorability by design?

Quasi-experiments

• Observational studies
• Data structured such that we can credibly make causal claims
• We can treat them as experiments but they are not

Examples:

1. Regression discontinuity design (RDD)

2. Difference-in-differences (DID)

RDD ingredients

• \(Y_i\): outcome

• \(X_i\): score or running variable

• \(c\): cutoff or threshold

• \(T_i\): Treatment indicator

Potential outcomes

\[ Y_i = (1 - T_i) Y_i(0) + T_i Y_i(1) = \begin{cases} Y_i(0) & \text{if } X_i < c\\ Y_i(1) & \text{if } X_i \geq c \end{cases} \]

Sharp RDD

Called sharp because treatment assignment is deterministic at the cutoff

Interpretation: Two approaches

1. Local randomization

2. Continuity-based

Local randomization approach

• Bandwidth \(\mathcal{W} = [c−w,c+w]\)

• Treatment as-if random within \(\mathcal{W}\)

• ATE point-identified within \(\mathcal{W}\)

Local randomization approach

Requirements

1. Known probability distribution of scores within \(\mathcal{W}\) (\(\equiv\) random assignment)

2. Potential outcomes not affected by scores within \(\mathcal{W}\)

Local randomization approach

Estimation

• Difference in means within \(\mathcal{W}\)

Inference

1. Randomization inference

2. Normal-approximation (super-population)

Continuity-based approach

• ATE is point-identified at cutoff

• \(\tau_{SRD} \equiv E[Y_i(1) - Y_i(0) | X_i = c]\)

• But it does not exist!

• Still, we can approximate

Continuity-based approach

• ATE is point-identified at cutoff

• \(\tau_{SRD} \equiv E[Y_i(1) - Y_i(0) | X_i = c]\)

• But it does not exist!

• Still, we can approximate

\[ \lim_{x \downarrow c} E[Y_i | X_i = x] - \lim_{x \uparrow c} E[Y_i | X_i x] \]

Local polynomial point estimation

Steps

1. Choose polynomial \(p\) and kernel function \(K(\cdot)\)

2. Choose bandwidth \(h\)

3. Fit \(\widehat \mu_+\) and \(\widehat \mu_-\) via weighted least-squares (based on \(K(\cdot)\))

4. Estimate: \(\widehat \tau_{SRD} = \widehat \mu_+ - \widehat \mu_-\)

5. Inference: Correct for adaptive bandwidth selection

This a non-parametric procedure since most choices are automated to find optimal MSE

Polynomial \(p\)

Different polynomials yield different estimates

Kernel function \(K(\cdot)\)

\(K(\cdot)\) assigns weights to units based on distance to cutoff (triangular performs better)

Bandwidth \(h\)

Narrower: less bias, more variance. Wider: more bias, less variance

DID ingredients

• Time periods: \(t = \{1,2\}\) (Before/after treatment)

• Treatment: \(D_i = \{0,1\}\)

• Potential outcomes: \(Y_{i,t}(0) = Y_{i,t}(0, 0)\) and \(Y_{i,t}(1) = Y_{i,t}(0, 1)\)

Switching equation

\[ Y_{i,t} = D_i Y_{i,t}(1) + (1-D_i) Y_{i,t}(0) \]

Same as canonical potential outcomes framework but now with time periods

Causal estimand

Average treated effect on the treated (ATT) in \(t=2\)

\[ \tau_2 = E[Y_{i,2}(1) - Y_{i,2}(0) | D_i = 1] \]

• Cannot observe directly

• Cannot avoid selection bias

• But before/after setup allows for valid estimation

Causal estimand

DID estimation

\[ \widehat{ATT} = [\text{Mean}(B) - \text{Mean}(A)] - [\text{Mean}(D) - \text{Mean}(C)] \]

DID estimation

\[ \widehat{ATT} = \underbrace{[\text{Mean}(B) - \text{Mean}(A)]}_\text{Difference} - \underbrace{[\text{Mean}(D) - \text{Mean}(C)]}_\text{Difference} \]

DID estimation

\[ \widehat{ATT} = \underbrace{\underbrace{[\text{Mean}(B) - \text{Mean}(A)]}_\text{Difference} - \underbrace{[\text{Mean}(D) - \text{Mean}(C)]}_\text{Difference}}_\text{Difference-in-differences} \]

Rewrite as a regression estimator

Two time periods

\[ \begin{align} Y = & \beta_0 + \beta_1 \text{Treated} + \beta_2 \text{Post-treatment} + \\ & \color{purple}{\beta_3 \text{Treated} \times \text{Post-treatment}} + \varepsilon \end{align} \]

# Both are the same
lm(Y ~ Treated * Post-treatment, data = dat)

lm(Y ~ Treated + Post-treatment + Treated:Post-treatment, data= dat)

Rewrite as a regression estimator

Multiple time periods

\[ Y = \alpha_i + \alpha_t + \color{purple}{\beta_1 \text{Treated}} + \varepsilon \]

Known as the two-way fixed-effects estimator (TWFE)

lm_robust(
  Y ~ Treated,
  fixed_effects = ~Unit + Time,
  clusters = Unit,
  se_type = "stata", # faster computing
  data = dat
)

Assumption: Parallel trends

What if we break parallel trends?

What if we break parallel trends?

Challenge: Staggered adoption

See Roth et al 2023 and did package for details