Non-parametric estimators (one-sample)

class: center, middle, inverse, title-slide

.title[
# Non-parametric estimators (one-sample)
]
.author[
### Yue Jiang
]
.date[
### STA 490 / STA 690
]

---

### Representing survival data

Underlying data:
- `$T$`: Failure time, a non-negative random variable
- `$C$`: Censoring time, a non-negative random variable
Observed data for individual `$i$`:
- `$X_i$`: `$(T_i \wedge C_i)$`, the minimum of `$T_i$` and `$C_i$`
- `$\delta_i$`: `$1_{(T_i \le C_i)}$`, whether we observe a failure

**Our goal is to make inferential statements about** `$T$`.

---

### Survival function

The .vocab[survival function] is given by `$S(t) = P(T > t)$` and has the following properties:

- `$S(0) = 1$`
- `$\lim_{t \to \infty} S(t) = 0$`
- `$S(t_2) \le S(t_1)$` for `$t_2 \ge t_1$`

.question[
How might we estimate `$S(t)$`?
]

---

### Some assumptions

Suppose we observe each `$X_i$` and corresponding `$\delta_i$`

- `$\{(X_i, \delta_i)\}$` are i.i.d.
- `$T_i \perp T_j$` for `$i \neq j$`
- `$T_i \perp C_i$`

We do not make any distributional assumptions on `$T$` or `$C$`.

---

### Some more notation

Let the unique, ordered, observed failure times be given by

`\begin{align*}
t_1 < t_2 < \cdots < t_D
\end{align*}`

with `$d_j$` being the number of failure events observed at time `$t_j$`.

Let `$c_j$` be the number of censoring events in `$(t_j, t_{j + 1})$`, with unique,
ordered, observed censoring times given by

`\begin{align*}
c_{j_1} < c_{j_2} < \cdots < c_{j_{c_j}}
\end{align*}`

---

### Some more notation

Define the .vocab[risk set] at time `$t_j$` to be the `$Y_j$`, the number
of individuals at time `$t_j$` who are still "eligible" to fail at time `$t_j$`.

.question[
"Who" is still in the risk set at time `$t_j$`? What does it mean to still be
"eligible" to fail?
]

Let `$d_j$` be the number of failures at time `$t_j$`.

---

### The Kaplan-Meier estimator

Suppose we divide our timeline into a set of small intervals, perhaps small enough so that intervals contain at most one event (this isn't strictly necessary, but for now assume we don't have any tied failure times).

*(see board)*<br>

Then we have

`\begin{align*}
S(t) = P(T > t) &= P(T > t | T > v_v) \times \\
&\mathrel{\phantom{=}} P(T > v_v | T > v_{v-1}) \times \\
&\mathrel{\phantom{=}} \cdots \times \\
&\mathrel{\phantom{=}} P(T > v_3 | T > v_2) \times \\
&\mathrel{\phantom{=}} P(T > v_2 | T > v_1) \times \\
&\mathrel{\phantom{=}} P(T > v_1)
\end{align*}`

---

### The Kaplan-Meier estimator

For very small interval `$(v_{j-1}, v_j]$`, if this interval contains an observed
event time, then we have

*(see board)*<br>

`\begin{align*}
\widehat{P}(T > v_j | T > v_{j - 1}) = 1 - \frac{d_j}{Y_j}
\end{align*}`

That is, 1 minus the number who fail during this interval divided by the number
still eligible to fail at the beginning of this interval.

.question[
What is a good estimate of `$\widehat{P}(T > v_j | T > v_{j - 1})$` if someone does *not* fail during this interval?
]

---

### The Kaplan-Meier estimator

Thus, depending on our partition, we have

`\begin{align*}
\widehat{S}(t) = 1 \times 1 \times \left(1 - \frac{d_1}{Y_1}\right) \times 1 \times \left(1 - \frac{d_2}{Y_2}\right) \times \cdots \times (1 - \frac{d_i}{Y_i})
\end{align*}`

where `$t_i$` is the largest observed failure time `$\le t$`. That is,

`\begin{align*}
\widehat{S}(t) = \prod_{j: t_j \le t} \left\{1 - \frac{d_j}{Y_j} \right\},
\end{align*}`

where `$t_j$` are the unique death times `$\le t$`.

.question[
What might `$d_j/Y_j$` itself be a reasonable estimator of?
]

---

### Estimating the survival curve

Suppose we had a small study with the following data:

| Patient | Event Time | Event Type | 
| ------- | ---------: | ---------- |
| 1       | 4.5        | Failure    |
| 2       | 7.5        | Failure    |
| 3       | 8.5        | Censoring  |
| 4       | 11.5       | Failure    |
| 5       | 13.5       | Censoring  |
| 6       | 15.5       | Failure    |
| 7       | 16.5       | Failure    |
| 8       | 17.5       | Censoring  |
| 9       | 19.5       | Failure    |
| 10     | 21.5       | Censoring  |

---

### Estimating the survival curve

| `$t$`  | Risk Set | # Failed | # Censored | `$\widehat{S}(t)$` |
| ---: | -------: | -------: | ---------: | :----------: |
| `$0$`    | `$10$`       | `$0$`        | `$0$`          | `$1$`          |
| `$4.5$`  | `$10$`       | `$1$`        | `$0$`          | `$1 - \frac{1}{10} = 0.9$` |
| `$7.5$`  | `$9$`        | `$1$`        | `$0$`          | `$0.9 \times (1 - \frac{1}{9}) = 0.8$` |
| `$8.5$`  | `$8$`        | `$0$`        | `$1$`          | `$0.8 \times (1 - \frac{0}{8}) = 0.8$` |
| `$11.5$` | `$7$`        | `$1$`        | `$0$`          | `$0.8 \times (1 - \frac{1}{7}) = 0.69$` |
| `$13.5$` | `$6$`        | `$0$`        | `$1$`          | `$0.69 \times (1 - \frac{0}{6}) = 0.69$` |
| `$15.5$` | `$5$`        | `$1$`        | `$0$`          | `$0.69 \times (1 - \frac{1}{5}) = 0.552$` |
| `$16.5$` | `$4$`        | `$1$`        | `$0$`          | `$0.552 \times (1 - \frac{1}{4}) = 0.414$` |
| `$17.5$` | `$3$`        | `$0$`        | `$1$`          | `$0.414 \times (1 - \frac{0}{3}) = 0.414$` |
| `$19.5$` | `$2$`        | `$1$`        | `$0$`          | `$0.414 \times (1 - \frac{1}{2}) = 0.207$` |
| `$21.5$` | `$1$`        | `$0$`        | `$1$`          | `$0.207 \times (1 - \frac{0}{1}) = 0.207$` |

---

### Estimating the survival curve

| `$j$`   | `$t_j$`  | `$Y_j$` | `$d_j$` | `$\widehat{\lambda}_j$` | `$\widehat{S}(t)$` |
| ---:  | ---: | -------: | -------: | ---------: | :----------: |
| `$-$`   | `$0$`    | `$10$`       | `$0$`        | `$0$`          | `$1$`          |
| `$1$`   | `$4.5$`  | `$10$`       | `$1$`        | `$0.1$`          | `$0.9$` |
| `$2$`   | `$7.5$`  | `$9$`        | `$1$`        | `$1/9$`          | `$0.8$` |
| `$3$`   | `$11.5$` | `$7$`        | `$1$`        | `$1/7$`          | `$0.69$` |
| `$4$`   | `$15.5$` | `$5$`        | `$1$`        | `$1/5$`          | `$0.552$` |
| `$5$`   | `$16.5$` | `$4$`        | `$1$`        | `$1/4$`          | `$0.414$` |
| `$6$`   | `$19.5$` | `$2$`        | `$1$`        | `$1/2$`          | `$0.207$` |

We see that this estimator only changes at observed failure times, with the number of jumps equalling the number of unique failures.

---

### Estimating the survival curve

---

### Just for kicks

---

### Just for kicks

---

### Just for kicks

---

### Just for kicks

---

### Back to the DIG trial*

<br><br>
.small[*just because you're familiar with it already. We'll use more interesting data for Thursday's homework!]

---

### Kaplan-Meier estimates in R

```
##    ID TRTMT DWHF DWHFDAYS
## 1   1     0    1     1379
## 2   2     0    1     1329
## 3   3     0    1      631
## 4   4     1    0     1157
## 5   5     0    1      191
## 6   6     0    0     1620
## 7   7     1    0      903
## 8   8     1    0     1369
## 9   9     0    0     1747
## 10 10     1    0     1074
```

---

### Kaplen-Meier estimates in R

```r
dig_surv <- Surv(dig$DWHFDAYS, dig$DWHF)
dig_surv
```

```
##    [1] 1379  1329   631  1157+  191  1620+  903+ 1369+ 1747+ 1074+  694   178 
##   [13]  200   384+  236+ 1558+ 1551+  868+ 1385+  788+ 1320+ 1333+ 1473+  521+
##   [25] 1173+  823  1013  1039+ 1570+  856   195+   70  1369+   74  1500+ 1327+
##   [37] 1551+ 1622+  709    68+  996+ 1320+ 1588+  881+ 1450  1637+  964  1299+
##   [49] 1031    95   101+ 1495+ 1599+  631+ 1223+ 1704+  225   120  1699+ 1129+
##   [61] 1123+ 1284  1409+  125  1619+  442+ 1369+  627+  537+ 1606+ 1668+ 1348+
##   [73] 1220+ 1298+ 1360+  979   129  1083+   14  1301+  931+   62    71  1301+
##   [85]  154   776  1166+  977+  223  1047+  658  1081  1424+  219   870+ 1166+
##   [97] 1117   699   120  1006+   79  1501+ 1481+ 1525+ 1363+   24+ 1495+ 1350+
##  [109]   88+  836  1559+  986+  371   149+  152+  877+  880+  154+ 1199+ 1340 
##  [121]  633+  416    23   883   134  1193+ 1381+  181  1299+ 1493+  309  1356+
##  [133]  972+ 1451+ 1439+   56    46  1486+ 1054+  190+   96  1308+ 1536+  319 
##  [145] 1449+  380   800  1675+ 1311+  407   193+  841+ 1557+  327  1707+  280+
##  [157]  183+  170+ 1528+ 1242+   34  1216+ 1655+ 1528+ 1368+  431+  900+ 1333+
##  [169] 1404+ 1733+  599  1493+  916+ 1154+   94   354   156+ 1194+ 1691+  718 
##  [181] 1076+ 1445+   77  1055    19  1389+ 1213+  948+ 1473+   12+  239  1273+
##  [193]  877+ 1411+ 1439+ 1314+   75   865+  315  1612+  141   114+  902+ 1454+
##  [205]  244+  965+ 1325+  882  1046+ 1160+  840+  830  1383+  147+  603+   61 
##  [217]  879+ 1273+ 1268+  501   985+  790   531   545   411+  453   699+  379+
##  [229]  797   930+  398  1380+   78   104+  171  1552+ 1469+ 1371+ 1327+  407 
##  [241]  991+ 1655+  544+ 1013+  288  1012+   45     8  1266+ 1262+  752   150 
##  [253] 1284+ 1760+  493+  978+ 1482+  457  1437+  492    28  1011+   86   403+
##  [265] 1355+ 1399+  494   274   999+ 1026   325  1301+ 1398+  972    59    71 
##  [277]  999+   25   568   992+ 1402+   60   622   111  1312+   35+  887+  961+
##  [289] 1355+   26+  960   676  1074+  276   592  1567+  905+ 1122  1004+ 1173+
##  [301]    7+ 1402+ 1369+  352   175+ 1508+  224    34   852+ 1053+ 1143+  596+
##  [313]  149+ 1166+  813   155+  286+   75  1686+  770  1472+  502  1314+ 1588+
##  [325]  238+  121+  927+ 1532+  773  1565+ 1242+ 1329+ 1417+ 1202   323+  652 
##  [337]  455  1490+ 1046+ 1054+  692+  862  1549+ 1360+ 1369+  209+ 1495    31 
##  [349]  195+   14    13  1141  1017+ 1428   445+ 1710+ 1197    21   636+  353 
##  [361]  804+  243  1510+ 1398+  578+ 1032+  590  1334+  306  1445+  336  1032+
##  [373] 1132+  815+   69    25  1161+ 1658+ 1626+  204  1166   554+  911    10 
##  [385] 1515+  255    83+ 1333+ 1279+  933+ 1360+  798+ 1067  1616+ 1742+  349 
##  [397]  989+ 1279+  241  1446+  624+ 1086   968+ 1084   971+ 1470  1678+  101 
##  [409] 1592+   32+ 1343+  714+  366   249  1402+  941+ 1214+  204+  912+   41+
##  [421]  886+  270+  263+ 1579+ 1228+  323  1024  1430+  588+ 1342+ 1180+  694+
##  [433] 1312+ 1105+  631+ 1264+  899+ 1613+   87+ 1530+  138  1523+ 1718+ 1273+
##  [445]  945  1328+  581  1721+ 1033+  341+ 1571+    1    96   867+  921+ 1127+
##  [457]  111   294+ 1733+  605+ 1710+  638+  381   855   499  1552+ 1727+  753 
##  [469] 1370+ 1550+  582  1327+  786+ 1287+  669  1368+ 1018+  490  1181+  300 
##  [481]  275+  741  1266+  304  1458+  320  1144+ 1167+ 1005+  213  1341+ 1636+
##  [493] 1257+ 1343+ 1193+ 1388+ 1515+  905  1129   494  1076+ 1677+  680   268 
##  [505]  674+    3   639  1326+  457+   86+ 1202+  708  1685+ 1410+  712    72+
##  [517] 1417+ 1502+  321  1074  1236+ 1514+  188  1770+ 1348+ 1473+    2   707 
##  [529]  622  1476+ 1360+ 1188+  707  1452+ 1172+  991+ 1432+  620  1286+   57 
##  [541] 1497+ 1543+  645+ 1405+ 1241    63  1285+ 1528+ 1522+ 1019+  142+ 1327+
##  [553]  161   718   992+ 1124+  647     8    22+ 1042+  872+  748  1150+ 1227+
##  [565]  287+ 1628+ 1416+ 1656+  704  1075+  949+  953+ 1084+ 1348+  956+  593+
##  [577] 1587+  559+ 1606+  330  1089+  344  1277+  617  1707+  867+  949+ 1312+
##  [589]  234   367+  633   171  1557+ 1027+ 1439+  793   116   839  1544+  422 
##  [601] 1322+ 1530+  217+  827+ 1404+ 1578+  232+ 1340+  280   345   755+ 1228+
##  [613]  997+ 1192+  454+ 1378+ 1481+  295+ 1292+    4   909  1324+ 1133+ 1215+
##  [625] 1536+ 1598+ 1430+  871+  713  1042+  969+ 1693+  410   880+ 1654+ 1321+
##  [637] 1404+  147   579+ 1433+ 1405+  784  1600+ 1711+   39+ 1570+  669   116 
##  [649]  136  1339+  679+    9   854    67    52+ 1509+ 1669+  263+ 1453+ 1375 
##  [661] 1234+ 1558+  684   873+ 1353+ 1075+ 1710+   64+ 1168   556  1147+  867+
##  [673]  542+ 1571+ 1402+ 1428+  463+ 1052+   15  1157+  357   905+ 1558+  418 
##  [685]  630  1402+  230  1178+ 1215+ 1362+ 1508+  665   999+ 1135  1346+  410 
##  [697]  695   139  1076+ 1027+  192  1294+  259  1117+ 1766+  923+ 1335+ 1505+
##  [709]   93   894   918  1187+ 1657+  180   505   293  1042  1259+  237  1420+
##  [721] 1472+ 1647+  447    40  1630+ 1139+ 1587+ 1294+ 1318+ 1507  1180+  693 
##  [733]  558   869   545+  357   785  1507+  145  1181+ 1536+ 1440+  877+ 1650+
##  [745] 1132+ 1136  1049+    7  1235  1502+ 1424+  157  1396+  880+  338+  284 
##  [757] 1515+  336+  599     8  1014  1160+ 1011+ 1518+  303   169   943   614 
##  [769]  878+  372+ 1654+ 1357+  256  1265+ 1192+  939  1089+ 1447+  310+ 1153 
##  [781] 1122+  154   940+  701+  220  1399+  245   159    19   659   756  1196+
##  [793] 1068+ 1481+ 1017+  877   129   707+ 1537+  814   474+ 1510+   13   288 
##  [805] 1535+ 1124+ 1343+  110  1201+ 1431+  174+  508   119   638+ 1390+  406+
##  [817] 1166  1010+ 1693+ 1321+ 1675+   31  1523+  607   588   998+  203  1382+
##  [829] 1284+  596  1389+ 1201+ 1710+ 1424+  791   106  1409+ 1188+  867+ 1399+
##  [841] 1083+  345   852  1039+  247   692+ 1474+ 1546+  958+ 1733+  808   950+
##  [853]  868  1587+  534   831  1371+  322  1446+   51+   54   211+  338  1555+
##  [865] 1055+ 1259+   24+ 1181+  629+  196  1307+ 1279+ 1343  1208+ 1197  1080+
##  [877]  490+ 1319+  935+ 1592+   67  1570+ 1448+  283  1104+  418  1220+  635 
##  [889] 1056+ 1158+ 1124+  803     7  1395+  856+   36  1055+ 1054+  837  1678+
##  [901]   93  1214+ 1418+  916+ 1133+ 1553+ 1031  1451+ 1380+  186+ 1537+  268 
##  [913] 1577+ 1167+ 1544+  873+  907   141  1432+ 1700+ 1069+ 1495+ 1284+ 1699+
##  [925] 1102+  363   962+ 1311   975+   47+ 1279+  802+   43  1417+  710  1181+
##  [937] 1228+  380+ 1140+ 1545+ 1109+ 1676+  157  1103+  306   269+  327+ 1040+
##  [949] 1747+ 1594+ 1450   783+ 1169+ 1447+ 1449+   64  1496+  926+  271  1630+
##  [961]  409+  871+ 1146+ 1607+ 1517+  735  1501+ 1033+   78  1392+  143+  874+
##  [973]   31  1154+   25   642   371   908+ 1194+  233  1195+ 1698+ 1117+ 1677+
##  [985] 1271+ 1529+  868  1633+  161+ 1594+  302+  902+ 1476+ 1037+ 1186+  330 
##  [997]  249    16  1136+  648+  804  1500    25  1350+   40  1257+  913+ 1637+
## [1009] 1497  1108+ 1535+ 1117+  168  1074+ 1061+ 1609+ 1613+  201+  472     7 
## [1021] 1252+ 1621+ 1007+  229+ 1384+ 1082+ 1532+ 1500+ 1264+ 1111+ 1046+   56 
## [1033] 1523+ 1018+ 1476+ 1031   393  1475+   84+  159  1136+  578+   10    47+
## [1045]   14  1370+ 1054+ 1671+  534  1339+ 1286+ 1387  1551+ 1227+ 1132+  908+
## [1057]  139+ 1094    24   372+  328+  214  1216+  909  1542+ 1168+ 1595+ 1252+
## [1069] 1053+  408  1006+  115   230   615  1007  1201+  884+ 1552+  266  1489+
## [1081]  943+   17+  203  1574+   47+ 1648+  388  1355+   98   986+ 1206+  739 
## [1093] 1509+ 1108   147  1108+  793  1647+  123   887+ 1675+  523+  785   603 
## [1105]  299+  751  1348+   13  1432+ 1375+ 1196+  351+  976+  976+  898     1+
## [1117] 1474+  148    11+ 1054+ 1370+  678  1455+  175   693+ 1495+ 1167+  510 
## [1129]  483  1753+  915+  320  1185+  962+  291+ 1374+  825  1469+ 1188+ 1325+
## [1141] 1531+  658  1230+ 1381+ 1530+  238  1287+ 1001+  294   958+  174  1207+
## [1153] 1419   247+ 1698+  127  1705+  497  1199+ 1045+  107     2   246  1348+
## [1165]  700+   49  1285+  944  1282+ 1676+  577  1132+ 1334+ 1627+ 1160+ 1579+
## [1177] 1041+ 1599+  977  1305+ 1591+ 1340+  598+ 1133+ 1601+ 1227+ 1392+ 1689+
## [1189]  104+ 1538+ 1076+ 1383+ 1262+  433+   28  1509+  159   163+  156   209+
## [1201]  392   360+  170  1004+ 1360+ 1684+ 1403+ 1395+  911    38  1360+ 1223+
## [1213] 1538+  914+  103  1447+ 1070+ 1542+ 1271+ 1346+  155+ 1011+ 1588+ 1403+
## [1225]  276  1719+ 1558+ 1242+ 1719+ 1020+  159  1489+ 1447+   15+  768   712 
## [1237] 1705+  989+  595  1181+ 1455+  368+   32    82  1224+  728   200   270+
## [1249]   22  1423+  251+  153   734     7    30  1073+ 1483+  806   763   252 
## [1261] 1349+ 1591+  460  1662+  283  1234+  443+ 1676+  888+  286  1559+ 1663 
## [1273] 1356+  126+ 1391+ 1606+ 1010+  694+ 1327+ 1285    57  1557+ 1434+ 1584+
## [1285]  191   812  1579+   37   481  1138+  848+ 1291+ 1010+  172   474+ 1182+
## [1297]   90  1313+  418  1093   985+  899+  270  1418+  893+  943+    1+ 1046+
## [1309]  154  1119+ 1383+ 1340+  571  1200  1599+    2  1705+  405+  610+  703 
## [1321]   70   543   103   913+ 1017+ 1567+ 1623+ 1482+  129   189+  488+ 1354+
## [1333] 1302  1336  1671+ 1304+  154+  720+ 1437+  867+  793   644+ 1272+ 1717+
## [1345]  516+  267  1699+  193   209   746  1670+   77  1278+   57  1602+ 1316 
## [1357] 1076+   28   826  1131+  231    66  1266+  587   878+   71+ 1166+ 1014+
## [1369] 1447+  362   228   385+  209  1707+ 1152+  595    62  1536+ 1453+  426 
## [1381] 1112+  389+ 1423+   51+  723   216  1392+  260+ 1292+ 1599+  855  1158+
## [1393] 1299+ 1319+   55+ 1364   102    17+ 1453+ 1459+ 1308+ 1024+  124  1557+
## [1405]  280   206+  658  1496  1658+  415  1195+ 1060+  553+ 1634+  182  1544+
## [1417]  113   836   993+ 1161+ 1374+ 1530+   58+ 1351   231   940+ 1060+ 1328+
## [1429]   14   941   153+ 1194+ 1132+  764+  201  1153+ 1564+  669+  905+  149+
## [1441] 1628+ 1424+ 1454+ 1110   976   138   927+ 1558+  106+ 1269+  245  1076+
## [1453] 1171+ 1448+ 1481+ 1074+ 1176+  350  1391+ 1381+ 1089+  524  1482+ 1143 
## [1465]  763  1579+ 1119+  885+  148  1537+  387   191    25   708+  539   153 
## [1477]  413+ 1161+  598  1669+  357   908+ 1510+  268   151+ 1084+   27+ 1014+
## [1489] 1351  1089+   62   854+ 1374+ 1368+ 1606+ 1454+   81   678+    8   176 
## [1501]  887+ 1574+ 1027+ 1655+ 1291+   33  1188    86   914+ 1084    68   405 
## [1513]  217+ 1135   877+  210   660+  886+ 1486+  463  1517+   12    48  1209+
## [1525] 1235+ 1370+ 1208+  633  1648+ 1669+ 1402+ 1251+ 1234  1510+  616  1409+
## [1537]   43   879+  950+   15  1516+  692+  359  1368+ 1012+  473+ 1619+  473+
## [1549] 1531+   37  1108+  760   262+ 1196+ 1319  1598+ 1322+  740   117   944 
## [1561] 1564+  713  1530+ 1536+    9  1523+    5  1174+  530    31  1217+ 1319+
## [1573]  651  1516+  562+ 1072  1272+ 1160+ 1697+ 1118+  742+  472+   50+ 1628+
## [1585]  711+ 1530+  341  1223+  250+ 1091+ 1068+ 1361+ 1440+  970+ 1508+    3 
## [1597]  346   595+ 1474+ 1378   176   950+  204  1143+ 1213+  961+  916+  956 
## [1609]   55    10   121   661   143  1154+   32+ 1069+  356    63  1036   488 
## [1621] 1048+ 1598+ 1251+ 1342+ 1619+ 1103+ 1545+  694  1410+ 1312+   23  1523+
## [1633]  302   984+  913+ 1405+   32   887+  958    35   985+ 1048+ 1564+  814 
## [1645]  488    21   510+   63  1074  1167+  930+  161+ 1591+ 1424+  612+  490 
## [1657]   97  1154+ 1161+  953+ 1213  1118+   67  1187+ 1496+ 1355+   40  1682+
## [1669]   87+ 1013+ 1560+ 1098+ 1588+  186+ 1657+ 1500+  186  1201+  345+ 1264+
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## [1693] 1376+  879+ 1523+  887+  262+ 1641+  961+ 1672+  556   582  1252+ 1537+
## [1705] 1607+  152+  920+ 1564  1612+   52  1341+  634  1072+ 1612+  212  1262+
## [1717]  629    29  1509+ 1248+ 1584+  930+ 1055+  287+   51+  137+ 1178+  190 
## [1729]  984+ 1490+  111  1488+   41   970+  491  1032+  516  1465+ 1325+ 1363+
## [1741] 1042+  236   157  1396+   29   493+  288+  445   967+   36  1558+  217 
## [1753]  913+ 1367+   47   410+ 1279+  903+  651  1336+ 1396+ 1364+  213  1201+
## [1765] 1682+  308   675+  146   772  1250+ 1593+  881+  518+ 1179+  443+  415+
## [1777] 1207+  197  1033+ 1293+  221  1043  1146+   70   955+  250  1293   155 
## [1789]  470   187  1739+ 1689+  142+  154  1599+  758+  714+ 1008  1614+  230 
## [1801]  725   836  1391+  120  1142  1544+  879+ 1430+    8  1619+ 1523+   66 
## [1813] 1287+    2+ 1199+  950+ 1419+ 1348+ 1518+  105   851   971   234   991+
## [1825] 1166+   77    15  1349+  771  1011+   77    80+ 1535+  711  1056+  977+
## [1837] 1195+  157   382   244    81  1600+  663  1542+ 1122+  968   805    84 
## [1849]   86   658   515  1544+ 1242   551  1286+ 1129+ 1698+ 1348+  976+  122 
## [1861]  197   867  1355+ 1329  1166+ 1126+ 1109+  320   913  1486+   17+  338 
## [1873] 1508+  138+ 1662+  626  1259+   67  1342+  242   209  1726+ 1504+   81 
## [1885] 1473+ 1559+  318   963+  985+  891+  323+  471  1107  1339+ 1556+ 1187 
## [1897]  175  1177+   35  1704+   85   996+ 1012+ 1111+ 1614+  728+ 1425+ 1301+
## [1909] 1087+  971+ 1423+   45   847    13+  908+ 1208+ 1598+  363+   37   182+
## [1921] 1682+ 1327+  902+  443   596+   11     9  1251+  269  1159+   13  1201+
## [1933] 1250+ 1004+  247   110+ 1481+  206   556   257  1080+ 1241+ 1187+ 1193+
## [1945]  872+ 1551+  269+  151+ 1356+  185+  380  1305+  780+  291   610  1378+
## [1957]  563     1+  385  1725+ 1525+ 1122+ 1299+ 1222+  110+  644+  163    15 
## [1969]  213   229+ 1271+ 1508+ 1207  1273+ 1115  1530+  992+ 1060+ 1509+ 1572+
## [1981]   99+ 1313+  921   587   493+ 1545+  194+  716   117+ 1516+  474+  695 
## [1993] 1691+ 1272+ 1280+ 1300   899+  989+  857+  681+ 1371+  151  1574+ 1664+
## [2005]  335+ 1235+  961+ 1636+ 1546+ 1024+ 1409+ 1675+  990+  965+ 1437+ 1390+
## [2017]   84  1188+   73  1143+ 1510+  276  1278+ 1113  1257+    7   937+  642 
## [2029]  806+ 1128+  356+ 1479+ 1588+ 1003+  248   632  1535+  336   397  1500+
## [2041]   16  1566+  553+  928+ 1125+ 1524+   44  1517+ 1003+   33+ 1025  1291+
## [2053]  505  1329+  385+ 1598+ 1419+  168   439+  895+ 1357+ 1434+  196   952+
## [2065] 1405+ 1440+ 1088  1286+ 1678  1404+  139  1080+ 1089+   49   289   755 
## [2077] 1689+ 1110+  928+  435  1559+   61+  160+ 1179   521+  979+  774+ 1474+
## [2089] 1059+ 1118+ 1153+ 1194+ 1082+ 1140+  872+  426+ 1402+  369  1029+ 1307+
## [2101]  975  1621+ 1663+ 1552+ 1237+ 1684+ 1200+ 1321+ 1075+   46    40    35+
## [2113]  674  1201+ 1405+ 1496+ 1263+ 1532+ 1384+  134+ 1318+ 1077   962+ 1109 
## [2125] 1082+  439    26  1619+  993   454    56+  921+  231+   34   966   915+
## [2137]  125+  532+ 1059+ 1154+ 1032+ 1063  1159+ 1137+  191    59   518  1013 
## [2149] 1124   496   294+ 1326+ 1256+ 1451+  916+  971+ 1150+  742+ 1132+  681 
## [2161] 1396+ 1331+  781  1438+  789+ 1214  1370+ 1190    61+  320  1208+   98 
## [2173]   13  1633+ 1004+ 1500+ 1034+ 1550+  921+  462+   48   149  1517+ 1330+
## [2185]   58+  682   963+ 1580+  872+ 1382+  138+  247  1699+ 1577+ 1680+  647 
## [2197]   47    31   990+ 1168+ 1503+ 1391+ 1221+ 1487+  193+  715  1076+  886+
## [2209]  821+  346+ 1719+ 1378+  780+  714  1469+  497+   23  1473+   47   634 
## [2221] 1462+  795+ 1301+  346+ 1572+  985+ 1600+ 1305+  553+  462   843   892+
## [2233]  802+   14  1013+ 1117+  605   209+  663  1614+  397+ 1294+ 1005+  538+
## [2245]  616  1112+ 1150+  989+ 1055+ 1227+  115   275   206+ 1214+ 1319+  356 
## [2257] 1334  1504+  221   894+  943+  644+ 1150+ 1115+ 1609+  629+ 1222+ 1333+
## [2269]  172+ 1696+  941+ 1181+ 1018+   13   670   105+  566  1616+ 1147+ 1214+
## [2281]  694  1154+  867+ 1672+ 1483+   97  1361+ 1626+ 1359+  713  1577+ 1066+
## [2293] 1466   128   228+ 1314+  356  1707+ 1089+  941+ 1166+  844   892+  669+
## [2305] 1320+   26  1182+ 1123+  275  1299+ 1196+  374+  540  1203+  278+  808+
## [2317] 1420+  119   394  1622+ 1574+ 1273+  442   798   348+ 1053+  985+  639+
## [2329]  272  1357+ 1452+ 1333+ 1528+ 1619+  412   119+ 1062+ 1404+  433  1332+
## [2341]  189+  403+  108  1216+  666   721  1570+  898+  947   395    19  1319+
## [2353]  872+  956+ 1189+  362+ 1096+  675+ 1070+  307  1495+ 1595+ 1264  1735+
## [2365] 1481+ 1599+  372  1574+ 1585  1327+   23    35   917   298  1297+   24 
## [2377]  107+ 1143+  493   246   554  1532+ 1391+ 1174+  895+ 1574+  354    30 
## [2389]  185  1626+  572   657  1411  1556+   61   443   859   550   394  1042+
## [2401]  276    10  1053+ 1452+  342  1031+   42+   66    86   801   646  1601+
## [2413]  281   228+ 1528+  569   871+ 1473+  735+  104  1698+ 1028+  492   922+
## [2425]  363+  901   107  1110+  244+ 1333+ 1217+ 1356+  989+ 1115+ 1238+ 1363+
## [2437] 1167+  670   969+  229   656   313  1619+ 1237+ 1322+   95     8+ 1112+
## [2449]   24   185   185  1493+  986+  327  1084  1139+ 1154+   35  1002   782 
## [2461]  167    47+  921    15   276+   35   875   421   880+ 1006+ 1507+  216 
## [2473]  899+   75  1390+  208   602+  963+   41  1430+  276  1128+  984+  118+
## [2485]  805+ 1040+ 1429   118+ 1367  1301+  879+  968+ 1073+ 1558+  515+ 1451+
## [2497] 1343+  704   185   801  1361+  573  1382+ 1301+ 1185+ 1496+  218  1528+
## [2509]  390   119   272+ 1188+ 1025+  326   185   472   127+    6  1333+ 1257+
## [2521] 1600+ 1308+ 1007+  741+   31   423+ 1524+ 1249+ 1602+  997+   26   919+
## [2533]  691+  974  1474+  623     8   103+  950+  163    69  1528+  366   241 
## [2545] 1308+ 1661+  186   950+   76  1349+  319  1410+    1   149+  926  1619+
## [2557]  134+ 1208+  236  1516+ 1371+  144   565+ 1486+  870+ 1385+ 1409+ 1112+
## [2569] 1483+ 1480+  790+  208+ 1256+ 1111+ 1321+   11  1587+  480  1692+  452 
## [2581]   68    49  1084   878+  176   422  1273+  870+  101   973  1558+ 1577+
## [2593]  520  1476+  526+ 1313+  902+ 1126   599+ 1271+  930+ 1105+  277  1343+
## [2605]  759  1361+ 1311+  992  1360+ 1721+ 1644+  248   991+  357+ 1497+   11 
## [2617] 1453+   46  1041+ 1357+    5   269  1680+ 1213+  922+ 1501+ 1066+   56 
## [2629] 1074+ 1176  1389+ 1283+  126+ 1656+  964+ 1504+ 1201+  653+  828  1399+
## [2641]  276  1474+  477  1034+  929+  877+ 1111+ 1117+  880+ 1307+  695  1241+
## [2653]  263  1545+ 1579+  453  1060+ 1566+ 1495+  537   553+ 1080+ 1001  1272+
## [2665] 1053+  304+ 1220+ 1475+  306  1556+ 1215+  970+   53   411+ 1255+  855 
## [2677]  388  1370+  701   328+  217  1587+   99  1671  1476+ 1186+   81    33+
## [2689]   92   527+  389+ 1278+  867+  588   166+   31  1564+  484   527    54 
## [2701] 1600+   39   559  1571+  989+  102+  364   587   760  1529+ 1433+  487 
## [2713]  155+ 1202+ 1425+  193   884+  675+  448  1341+ 1081+  902+  143  1303 
## [2725]  281+  131  1530+  187+ 1382+ 1361  1360+  123  1112+  258  1634+ 1273+
## [2737] 1235+ 1143+ 1497+  142  1545+ 1168+  354+ 1272+  833   124  1479+ 1150+
## [2749] 1553+  372   232   969+ 1397+  866+  907+  985+  943    21     6  1423+
## [2761] 1272+  801+ 1144+ 1000+   50   994+   66   571    10  1304+ 1578+ 1557+
## [2773]  335+  992+  650+  336+ 1196+ 1636+  258  1152+  391+   85  1390+ 1298+
## [2785] 1052  1530+ 1560+   74  1517    16  1525+  403+ 1362  1643+  118  1651+
## [2797]  521+  865+ 1391+ 1720+ 1006+ 1399+ 1293+  232  1399+  629   948+  723+
## [2809] 1357+ 1649+ 1481+  361   928+  614+  582  1298+ 1355+  406   245    97+
## [2821]  318   997   130+  161  1137+  473    86  1042   886+   43   870+  892+
## [2833] 1237+  123  1318  1363+  708  1325+  958  1038+  929+  601   117  1143+
## [2845] 1003+  567  1231+   81  1602+  135   102+  307+  676   871+  427  1713+
## [2857] 1599+  894+   40   364  1300+ 1405+  627   128  1057  1143+ 1502+  963+
## [2869] 1517+  315  1546+ 1142   515+ 1200+ 1606+ 1601+  848    99  1614+  936+
## [2881] 1495+ 1271  1059+ 1174+ 1354+  955   366   250+ 1571+   22+ 1446+ 1124+
## [2893] 1563+ 1619+   81   921+ 1397+  823  1154  1112+ 1083+   67  1256+ 1209+
## [2905] 1262+ 1040   798  1642+  590+ 1678+ 1622+ 1508+  258   623    30  1066 
## [2917]  731+   31  1154+  328   565+ 1416+  228   921+  923+ 1712+   15  1264+
## [2929]  233    70   246   197   596  1640+  147  1224+  547    78  1383+ 1317 
## [2941]   70    99  1202+ 1570+  906+  259  1360+ 1635+ 1079   208+  631  1588+
## [2953] 1417+ 1532+  343  1430+  992+  189   762   376  1462+  410+   27     7 
## [2965] 1040   870+  439+  976+  399   963+  183  1658+ 1571   114  1193+    1+
## [2977]   99   962+   43  1369+  772  1382+  113    30  1693+  930  1025+   48 
## [2989] 1206  1306+  259  1349+ 1580+ 1194+ 1580+  659   394    48+  513+  901+
## [3001]  550    31  1273+  906+  704   621+ 1147   898+ 1469+ 1495+  324+ 1144+
## [3013]  404+  935+ 1529+ 1203+ 1251+  202+  282  1696+ 1486+ 1518+  150    15 
## [3025]  544+  438+  134+ 1312+ 1346+ 1370+  948+  425  1119+ 1444+  182    48 
## [3037] 1040+  444   879+ 1770+ 1615+ 1300+  384   949+ 1404+  526  1404+  143+
## [3049]   62+ 1451+ 1493+ 1027+ 1119+ 1108+ 1206+  948+ 1189+   91   661   991+
## [3061]  416   126  1046+  268  1048+ 1558+  586    48   171  1404+ 1657+  545+
## [3073]   42  1178+ 1266+ 1683+ 1123+ 1199+ 1038+ 1301+  968+ 1518+ 1672+ 1564+
## [3085]  898  1120   893+ 1556+  374  1383+  173  1418+  241  1300+  351+  736+
## [3097] 1314  1374+  131   252  1517+  802+  572   895+ 1126+  254  1328+ 1418+
## [3109]   17  1525+ 1390+  478+ 1370+ 1022+ 1566+  567   114+  142+ 1017+ 1663+
## [3121] 1199+  676  1208+  211   702   205+ 1523+   64  1474+  379    27   793 
## [3133] 1020+   22+  329  1089+  240    24+ 1432+  910   318  1019+ 1031+  898+
## [3145]  794+ 1192+ 1055+   46  1201+  113   628  1579+ 1150+  260+ 1270+  137+
## [3157]  907+ 1734+ 1536+  900  1231+ 1588+  874  1154+ 1514+   69   892+  681 
## [3169]  389+  777+ 1027   873+   51   366+ 1249+ 1524+ 1065+ 1312+ 1747+ 1165+
## [3181] 1126+  903  1122+ 1707+  889   966+ 1501+  722+ 1230   145  1181+ 1571+
## [3193] 1305+  183   885+  294  1141   942+ 1675+ 1196+ 1227+ 1012+ 1713+  532 
## [3205] 1074    69+  873+  968+ 1490+ 1262+ 1425+ 1522+    6   985+ 1199+ 1432+
## [3217] 1103+ 1266+ 1577+ 1602+ 1703+ 1532+  161  1203+ 1389+ 1455+ 1292+    2 
## [3229]  223   340  1695   867+    4  1450+   94+  969+ 1504+ 1490+ 1523+ 1564+
## [3241] 1572+  134  1429   882  1026+ 1133+ 1090  1017+  885+ 1000+ 1286+ 1476+
## [3253]  665  1388+ 1508+  969+  937+ 1168+ 1571+ 1383+ 1550+   22     4+  148 
## [3265]   38  1545+   18  1718+ 1650+  982+  868   163  1301+ 1514+  540  1363+
## [3277] 1187+  126  1531+ 1656+ 1115+ 1003  1749+  923+  269+ 1480+ 1110+ 1579+
## [3289] 1325+  374+   28    49+   39  1503+ 1033+  637   430+ 1159   219  1427+
## [3301] 1497+  395  1035+  230  1363+ 1335+ 1054+   73   972+  395  1371+  396 
## [3313]   50  1537+ 1341+ 1633+ 1501+  871+  892+ 1151+  651+  112+  847   176 
## [3325]  119    26    47  1599+ 1521+  663+ 1243  1437+ 1516+ 1186    65   858 
## [3337] 1234+ 1319+  890    12    95+  508+ 1231+ 1486+ 1375+ 1073+  926+ 1188+
## [3349] 1497+  394  1108+  871+ 1657+   24  1622+  804+  441+  386    98+ 1308+
## [3361] 1209+ 1643   968+ 1404+ 1245    55   943+  371+ 1661+  894+ 1242+ 1423+
## [3373]  816    24   491  1398+  789  1439+  836  1437+ 1313+  968    15  1041+
## [3385]  969  1593+   97+  934+ 1046+  400+  527+ 1061+ 1048+ 1034+   72+ 1448+
## [3397]  189  1189+  954+  937   271+  248   710   553   557   454   136  1629 
## [3409]  503+  507+ 1500+  286    95+ 1418+ 1334+   22   511  1535+ 1090+  187+
## [3421] 1173+  589  1285+ 1398+  395   929+ 1411    87   105  1158+  369+ 1322+
## [3433]  178  1216  1117+  171+ 1675+ 1621+  839  1672+   11  1724+  878+  292 
## [3445]  834  1318+  434  1406+ 1496+  463   107  1710+  870+  214+  134  1573+
## [3457]   32  1160+ 1389+ 1391+ 1609+ 1110+ 1569  1046+   24   121   638   273 
## [3469] 1404+ 1633+  731+ 1620+ 1356+ 1404+ 1207+  126  1529+  487  1311+ 1552+
## [3481]  363  1109+  332+  768   867+  537+  351   821   967+  632    64  1650+
## [3493] 1368+ 1068+ 1427+  859   425+  971+  956+  392  1355+ 1614+ 1592+   56 
## [3505] 1236+ 1066+ 1081+ 1481+ 1343+ 1174+ 1194+ 1298+ 1118+  334   581   786 
## [3517] 1514+ 1160+ 1493+  929+  774   556   887+ 1279+  870+ 1000+   49   886+
## [3529]   11   731   202  1437+   84   929+  835  1110+  895+  125   915+ 1689+
## [3541] 1153+  958+  820+ 1375+  824+  397+  434+ 1159+ 1041+ 1294+    8   444 
## [3553] 1551+ 1355+  310   892+ 1781+  884   289+ 1341+ 1174+  357  1182+ 1301+
## [3565] 1128+  987+  892+ 1661+ 1473+ 1187+  626   448+ 1416+  285   688  1629+
## [3577] 1339+ 1075+ 1111     5  1528+ 1509+   17  1357+ 1486+  942+  558    40 
## [3589]    9   533  1399+   11  1426+  472   939+ 1725+ 1182+   97+ 1607+  222 
## [3601] 1592+    1   286   773   749+    3   458   581  1482+  407+ 1115+ 1340+
## [3613]  577   214+ 1076+ 1068+  463  1447+  873+  193+ 1607+ 1245+ 1187+  480 
## [3625]  870+  153   109   373+   48   601   197+ 1193+ 1129+ 1636+ 1277+ 1150+
## [3637] 1483+ 1314+ 1083+ 1649+   92  1377+ 1431+  343+ 1234+ 1475+  112+ 1433+
## [3649] 1341+  517   704+ 1518+  860+ 1677+  607+ 1174+ 1577+ 1565+  264+ 1027 
## [3661]  946+   90   365  1055+  352+ 1040+ 1661+ 1201+ 1360+ 1588+   95+ 1607+
## [3673] 1306+ 1609+  192  1273+  250+  253  1463   843   229  1689+  131  1019+
## [3685]  726  1550+  226   809  1411+ 1374+  447+  934+  799+   39  1620+  825 
## [3697] 1514+   24  1489+ 1689+ 1405+  540   693+  983+  797  1088  1125+ 1223+
## [3709] 1481+  318  1353+  391+ 1328+ 1684+  117   339   173   454  1417+  938 
## [3721]  297+  163   844  1227+  368   576+  965+ 1004+   98  1677+   53   228 
## [3733] 1320+  307   528  1504+  262+ 1462   961  1075+ 1546+ 1152+ 1476+ 1182+
## [3745]  107  1216+  885  1137+  446+  588  1063+ 1163+ 1122+ 1399+ 1416+ 1156+
## [3757] 1546+  315+    2+ 1209+ 1188+    6    41+ 1042+    8   406  1203+ 1069+
## [3769]  200   116   478  1186+ 1559+   33  1132+ 1487+ 1104+ 1102+  986+  825 
## [3781] 1375+ 1525+  911  1308+ 1529+  118  1098+ 1156   119+  986   140    36+
## [3793]  433    32   952   898+ 1488+ 1444+  543+  886   174+ 1130  1566+ 1391+
## [3805] 1360+  850    67+ 1198+ 1733+   59   891+  792   438  1341+ 1108+ 1619+
## [3817] 1322+ 1525+  828    60+  957+  939  1459+ 1565+ 1496+  119   289   801 
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## [4597] 1516+ 1536+ 1256+ 1056+  432  1129+ 1025+ 1240+ 1452+  176  1328+  941+
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## [4645]  541+ 1196+ 1256+  265  1249+  229+ 1524+ 1600+  600  1125+  766   224 
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## [4681] 1406+ 1411+  253+  589+ 1159+  787  1599+  952+  244  1259+  211  1161+
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## [4825]  874+  178+ 1566+ 1083+ 1553+ 1010  1452+  648+   28    71  1551+  594 
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## [4957] 1147+   55     6  1665+  934+ 1507+ 1453+ 1243+ 1341+ 1208+ 1167+ 1173+
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## [5077]  330  1322+    8   468  1244+  598  1377+  727  1452+ 1012+  574   477 
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## [5221]  683   416+ 1101  1403+ 1236+ 1146+  413   342  1285+  691  1382+  886+
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## [5245]  170+  514  1573  1476+ 1347+ 1017+ 1224+ 1040+  209  1567+  980  1493+
## [5257]  146  1421    98  1285     7   947+ 1382   537    21   666  1255+ 1154+
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## [5317]  213+ 1348+  511+ 1501+ 1294+ 1151+ 1452+ 1396  1613+ 1367+ 1333+  965+
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## [5341]  923+ 1420+  985+ 1528+ 1327+  285  1563+ 1496+  845   888+  925   852+
## [5353] 1377+ 1489+ 1724+  327+  329   966  1620+ 1186+  677   733   879+    6 
## [5365]   77   153   315  1116+ 1341+  351   491  1319+ 1458+   69    80   956+
## [5377]  166  1120+ 1514+ 1006+  912+ 1629+  666+ 1614+  908+  315  1587+  581+
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## [5449] 1266+ 1068+    3+ 1740+ 1035+  167+  943+  822  1542+  251  1474+  958+
## [5461] 1209    84   999  1377+ 1147+  371   298+  187+    1   926   533  1136+
## [5473]  831   296  1420+  576   575+ 1069+  988  1675+ 1218   357+ 1258+  366 
## [5485]   36  1297+  327  1388+ 1503+ 1515+ 1377   863+ 1090+  628  1053+ 1007+
## [5497] 1364+ 1146+  119+ 1082+ 1333+   32  1214+  110+  102   414   612  1378+
## [5509] 1395+ 1649+  949+  622+ 1340+  867+  234   976+ 1061+  126   485   904 
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## [5533] 1502+ 1234+   82  1599+  714+ 1000+ 1602+  130     5   182   353  1052+
## [5545]  355  1601+  840+ 1690+  943+  781+ 1256+  340+  304+ 1599+   74+   77 
## [5557] 1207+  527+ 1558+  238  1735+  491  1622+  923  1130   444  1070+   27+
## [5569]  962+ 1215+ 1367+ 1642+  860+ 1263+  979+ 1725+ 1369+   91    15  1134 
## [5581]  943+ 1434+ 1033+ 1448+  902+ 1525+  188+  123   804   796  1399+ 1083+
## [5593] 1025+  752+  185  1497+  822+  950+  307+  416   928+   45  1292   934+
## [5605]  344+  815+ 1493+ 1721+ 1587+  723  1032+  334   826  1212  1416+  370 
## [5617] 1567+  789   997+  919  1123+ 1146+  821+  664   859  1486+  523  1147+
## [5629]  175  1151+   80+ 1622+ 1276  1392+ 1530+ 1154+  301+  274  1503+   10 
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## [5653] 1357+  447+  975+ 1607+ 1514+ 1161   256  1567+ 1530+   41+ 1522+ 1504+
## [5665]  339  1551+ 1334+   59+  804+ 1151+  124+ 1188+ 1474+ 1032+ 1222+ 1427+
## [5677] 1530+ 1074   880+  880+  610   805   875   287+  790  1193+ 1299+ 1691+
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## [5701] 1341+ 1411+ 1124+   24   486  1551+ 1437+  931  1247  1332  1196+  268 
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## [5725]  790+ 1521+ 1133+ 1000+ 1119   385  1454+ 1682+    3  1240   105  1670+
## [5737] 1599+ 1084+ 1418+  442   921+  935+   23  1086  1215+  702   902+ 1010+
## [5749] 1348+ 1341+   39   519  1339+  898+ 1354+ 1164+   72  1172+  715  1411+
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## [5785]  942+ 1355+ 1473+  897+ 1469+   76   392  1602+ 1069+   24+  104    21 
## [5797]  908+ 1251+    1+ 1131+  949+ 1118+ 1416+  392   731  1069+ 1348+ 1010+
## [5809] 1417+  812  1224  1307+ 1102   168  1012+ 1124+   11  1182+  950+ 1011+
## [5821] 1073+  405   677   351   293   360   985+ 1585+  940+ 1574+  792+  283 
## [5833] 1395+ 1018+  425  1182+  112   425   160  1280+   54+  990   507  1528+
## [5845] 1160    71   275   709  1480+ 1440+  204   335   975+  135+ 1588+  970 
## [5857] 1621+  972+  728   636  1335+  635+ 1580+ 1112+ 1542+  910   168+ 1563+
## [5869]   26   112   893  1405+  336+  883   314    22   391  1691+  154  1433+
## [5881] 1138   148  1446+ 1703+  734  1132+ 1143+  577  1131+  984  1175   989+
## [5893] 1132+  933+ 1521+  857  1036+ 1433+   63   174  1188+  836   304   139+
## [5905] 1019+   62  1434+  928+  206+ 1097+  747  1320+ 1343+ 1423+   51  1035+
## [5917]  929+   51   329  1146  1518+   44  1363+  941+ 1455+  148   110+ 1496+
## [5929]   52  1105+  390   646  1440+  840+  259    88   317   941+ 1328+  375 
## [5941] 1553+ 1040+   70   278+  581+ 1171+  273  1455+ 1000+  694+   21   890 
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## [5989]  655  1390+ 1517+ 1377+ 1074+ 1262+   74   695+  200  1150+ 1355  1728+
## [6001]  457  1136+  330    53   224   655    21  1091   927+ 1472  1419+ 1486+
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## [6025]  906+   22   323  1487+    1   899+ 1398+ 1615+ 1504+ 1318+  124   389+
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## [6073] 1556+   13    17  1250+   99   979+  408+   22   947   270  1474+  419 
## [6085]   70+ 1556+  958  1713+ 1622+ 1417+ 1689+ 1313+  938    15+  887+  181 
## [6097] 1248+  544+ 1614+  286  1257+  305   164  1482+  479  1355+  952+ 1689+
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## [6121]  287+ 1615+ 1507+ 1515+  196+  129   602+  152+   32  1445+ 1552+ 1482+
## [6133]  921  1312+ 1629+ 1411+ 1334+ 1525+ 1273+  161  1424+  940+   79   901+
## [6145]   64   410  1297+ 1336+ 1564+  884+ 1378+   36  1249+  291  1243+  383+
## [6157]  840+  345+ 1018+  728   932+  673    19   201    61  1339+  117   278 
## [6169] 1321+ 1156  1076+  759+  970+ 1124+ 1206+  700  1503+ 1270+   54+ 1080+
## [6181] 1623+    1   906  1361+ 1423+ 1669+  894+  538+  384   118+ 1672+ 1374+
## [6193]  958+ 1412+  937+ 1287+ 1265+ 1059+ 1433+ 1339+ 1592+ 1012+ 1194  1426+
## [6205]  884+  941+ 1215+ 1584+  120  1578+ 1528+ 1572+ 1153+  937  1343+ 1333+
## [6217] 1490+  913   412    22   264+ 1118   491+   30  1140+ 1140+  854+ 1399+
## [6229]  211   413   784+  225+ 1433+  609+  871+  173   998    39   858   874+
## [6241]   87  1138+ 1118+  292+   40+ 1200+   15   463+ 1029   518   520  1621+
## [6253]  998+  232+  895  1206+ 1292+ 1115+ 1628+ 1017+ 1229+ 1259+ 1417+ 1066+
## [6265] 1623+ 1318+ 1496+  266  1166+   63+  486+  494   977+  980+ 1439+ 1005+
## [6277]  299   549+ 1061+  663+  941+  984+ 1509+ 1370+  781+ 1046+ 1174+   10+
## [6289] 1487+ 1012+  722+ 1479+  323   149+  392+ 1299+ 1571+  244   173+  880 
## [6301] 1448+ 1055+ 1350  1571+  881  1431+ 1665+ 1489+ 1283  1173+ 1152+  372 
## [6313] 1277   887+  743+ 1273+  468  1397  1488+ 1068+  667   757+ 1041+  396+
## [6325] 1558+ 1363+  724   474   214  1271+  480  1137+  772   928  1635+ 1426+
## [6337]  495   298+ 1278+  971  1341+ 1599+ 1112+  134   385  1397+ 1257+ 1271+
## [6349]  953+  796    30+ 1420+ 1509+  159+ 1519  1066+ 1187+ 1719+ 1356+  609 
## [6361]   35    32  1216+  327  1215+   10   134   475+ 1179+  982+    8   720+
## [6373] 1654+  234  1278+  474   968+ 1384+ 1246  1277+  965+    1    97   354 
## [6385]  758+   83   677+ 1091+  962   110  1504+  106     5   325  1570+ 1253 
## [6397]  725+  936  1059+ 1663+ 1274+  992+ 1334+ 1593+ 1654+  720   122  1388+
## [6409]  645+  119+   29   484  1293+  269  1202+  651   416  1488+ 1137+ 1502+
## [6421]  571  1565+ 1437+ 1580+ 1045+  873+ 1298+ 1602+  841+ 1108+ 1273+ 1292+
## [6433]  864  1083+  878+   59  1287+ 1259+ 1411+ 1406+ 1069+ 1083+  873+ 1355+
## [6445]  139   992   383   915+ 1293+ 1144+ 1203+ 1481+  998+ 1368+   67   979+
## [6457] 1495+  426  1396+ 1034    17  1474+ 1150+  100+   74    62+  228    73 
## [6469]  226   860+ 1234+ 1648+  877+  667   659+   36  1041  1285+  174  1056+
## [6481]  596  1155   484  1348+  999+ 1655+ 1035+ 1474+ 1411+  875+  951+ 1284 
## [6493]  155  1671+  333  1431+ 1591+  754   130   250   908+ 1587+  111   472 
## [6505] 1118+ 1489+  593   508+ 1290+  231   221   125   977+  599+ 1566+  990+
## [6517]  568+ 1113+   84+ 1556+  810+ 1570+  244+  902+  920+ 1761+ 1119+ 1091+
## [6529] 1399+ 1105+ 1616+  307+  574   892+   26   877+  239    91   714+  515 
## [6541] 1389+   43    94   943+  168+  581   307   369  1350+ 1523+ 1098+  999+
## [6553]  202+ 1164+ 1206+ 1605+ 1070+  185  1627+  410    15  1286+  962+   19+
## [6565]  494  1137+  792  1192+   28+  288   212    60+ 1016+ 1565+ 1208+  317+
## [6577] 1308+ 1675+ 1205+ 1000+ 1268    34  1406+ 1021  1313+  140   905+ 1427+
## [6589]  627+  605   575  1654+ 1515  1479+  847+   22   211+ 1607+ 1425+ 1502+
## [6601] 1161+ 1651+ 1385+ 1164+ 1054+ 1000+ 1062+  885   471  1342  1740+ 1377+
## [6613] 1341+  208+  413+ 1541  1326+ 1155   285  1052  1007+ 1515+ 1698+ 1290+
## [6625]  589   155+  462  1588+  744   777+  456  1419+ 1004+  542+ 1053+ 1727+
## [6637]  532+  512+  359+   13   876  1378+ 1047+ 1006+ 1332+  511  1059+ 1364+
## [6649]  655+  730  1311+ 1595+ 1196+  337  1447+  361  1728+ 1472+  259+ 1389+
## [6661] 1203+  101  1656+ 1445+ 1019+  706   481  1164+ 1042  1432+  163+  599 
## [6673]  253+ 1682+ 1472+ 1439+  986+  671+  994   134+   36    21  1411+  752 
## [6685] 1155+ 1497+ 1166+  959+ 1005  1264+  494  1403+ 1144+  930+ 1388+ 1504+
## [6697]  889   504+  324+ 1035+ 1010  1217  1191   179+  495+  690     2    61 
## [6709] 1417+  829  1425+ 1682+  195   608   431  1238+  970+  893+  681+  851+
## [6721]    6  1440+ 1700+  110  1320  1369+ 1507+ 1152+ 1207+ 1180+  370   136 
## [6733] 1187  1213+   96   396   576    89   841  1587+   93+   61  1584+  170 
## [6745]   18   568  1556+   29  1304+   98    42+  538+ 1152+  273  1231+  151 
## [6757]  234  1217+  965+ 1713+ 1652   861   518   247  1294+ 1612+  119    38+
## [6769]  525   109  1448  1164+  140  1431+ 1019+  885+ 1509+  683  1552+   73+
## [6781] 1528+   37  1472+ 1388  1139+  690  1055  1067  1448+  783  1195+  494 
## [6793]  507  1114   137   546  1419+  549   515  1738+
```

---

### Kaplan-Meier estimates in R

.pull-left[

```
##    ID TRTMT DWHF DWHFDAYS
## 1   1     0    1     1379
## 2   2     0    1     1329
## 3   3     0    1      631
## 4   4     1    0     1157
## 5   5     0    1      191
## 6   6     0    0     1620
## 7   7     1    0      903
## 8   8     1    0     1369
## 9   9     0    0     1747
## 10 10     1    0     1074
```
]

.pull-right[

```r
head(dig_surv)
```

```
## [1] 1379  1329   631  1157+  191  1620+
```

```r
dim(dig_surv)
```

```
## [1] 6800    2
```

```r
head(dig_surv[,1])
```

```
## [1] 1379 1329  631 1157  191 1620
```

```r
head(dig_surv[,2])
```

```
## [1] 1 1 1 0 1 0
```
]

---

### Kaplan-Meier estimates in R

```r
dig_fit <- survfit(Surv(DWHFDAYS, DWHF) ~ 1, data = dig)
dig_fit
```

```
## Call: survfit(formula = Surv(DWHFDAYS, DWHF) ~ 1, data = dig)
## 
##         n events median 0.95LCL 0.95UCL
## [1,] 6800   2332     NA      NA      NA
```

.question[
Why are there `NA`s in the output above?
]

---

### Kaplan-Meier estimates in R

```r
summary(dig_fit)
```

```
## Call: survfit(formula = Surv(DWHFDAYS, DWHF) ~ 1, data = dig)
## 
##  time n.risk n.event survival  std.err lower 95% CI upper 95% CI
##     1   6800       8    0.999 0.000416        0.998        1.000
##     2   6787       6    0.998 0.000550        0.997        0.999
##     3   6779       6    0.997 0.000657        0.996        0.998
##     4   6772       4    0.996 0.000720        0.995        0.998
##     5   6767       7    0.995 0.000818        0.994        0.997
##     6   6759       8    0.994 0.000917        0.992        0.996
##     7   6751       9    0.993 0.001016        0.991        0.995
##     8   6741      10    0.991 0.001116        0.989        0.994
##     9   6730       4    0.991 0.001154        0.989        0.993
##    10   6726       7    0.990 0.001217        0.987        0.992
##    11   6716      11    0.988 0.001309        0.986        0.991
##    12   6704       3    0.988 0.001333        0.985        0.990
##    13   6698       9    0.986 0.001403        0.984        0.989
##    14   6687       8    0.985 0.001462        0.982        0.988
##    15   6679      11    0.984 0.001539        0.981        0.987
##    16   6666       4    0.983 0.001567        0.980        0.986
##    17   6661       5    0.982 0.001600        0.979        0.985
##    18   6653       4    0.982 0.001626        0.979        0.985
##    19   6649       7    0.981 0.001670        0.977        0.984
##    20   6640       2    0.980 0.001683        0.977        0.984
##    21   6637       8    0.979 0.001732        0.976        0.983
##    22   6629       9    0.978 0.001785        0.974        0.981
##    23   6617      10    0.976 0.001843        0.973        0.980
##    24   6605       9    0.975 0.001893        0.971        0.979
##    25   6592       8    0.974 0.001936        0.970        0.978
##    26   6584       6    0.973 0.001968        0.969        0.977
##    27   6577       3    0.973 0.001984        0.969        0.976
##    28   6572      10    0.971 0.002035        0.967        0.975
##    29   6561       5    0.970 0.002060        0.966        0.974
##    30   6556       6    0.969 0.002090        0.965        0.974
##    31   6549      13    0.968 0.002153        0.963        0.972
##    32   6536      11    0.966 0.002205        0.962        0.970
##    33   6523       3    0.965 0.002219        0.961        0.970
##    34   6518       5    0.965 0.002242        0.960        0.969
##    35   6513       7    0.964 0.002273        0.959        0.968
##    36   6504       8    0.962 0.002309        0.958        0.967
##    37   6495       4    0.962 0.002326        0.957        0.966
##    38   6490       3    0.961 0.002339        0.957        0.966
##    39   6486       9    0.960 0.002378        0.955        0.965
##    40   6474       9    0.959 0.002416        0.954        0.964
##    41   6464       2    0.958 0.002424        0.954        0.963
##    42   6459       2    0.958 0.002432        0.953        0.963
##    43   6455       7    0.957 0.002461        0.952        0.962
##    44   6448       3    0.957 0.002474        0.952        0.962
##    45   6445       5    0.956 0.002494        0.951        0.961
##    46   6440       7    0.955 0.002522        0.950        0.960
##    47   6433       4    0.954 0.002538        0.949        0.959
##    48   6425       9    0.953 0.002573        0.948        0.958
##    49   6415       6    0.952 0.002596        0.947        0.957
##    50   6407       5    0.951 0.002615        0.946        0.957
##    51   6401       4    0.951 0.002631        0.946        0.956
##    52   6393       3    0.950 0.002642        0.945        0.956
##    53   6389       4    0.950 0.002657        0.945        0.955
##    54   6384       3    0.949 0.002668        0.944        0.955
##    55   6379       3    0.949 0.002679        0.944        0.954
##    56   6375       4    0.948 0.002694        0.943        0.954
##    57   6370       3    0.948 0.002705        0.943        0.953
##    59   6364       5    0.947 0.002723        0.942        0.952
##    60   6358       3    0.947 0.002734        0.941        0.952
##    61   6353       5    0.946 0.002752        0.940        0.951
##    62   6346       6    0.945 0.002774        0.940        0.950
##    63   6338       5    0.944 0.002792        0.939        0.950
##    64   6332       4    0.944 0.002806        0.938        0.949
##    65   6325       2    0.943 0.002813        0.938        0.949
##    66   6323       5    0.943 0.002830        0.937        0.948
##    67   6318       6    0.942 0.002851        0.936        0.947
##    68   6311       3    0.941 0.002862        0.936        0.947
##    69   6306       4    0.941 0.002875        0.935        0.946
##    70   6301       6    0.940 0.002896        0.934        0.945
##    71   6293       5    0.939 0.002913        0.933        0.945
##    72   6287       2    0.939 0.002919        0.933        0.944
##    73   6281       4    0.938 0.002933        0.932        0.944
##    74   6275       8    0.937 0.002959        0.931        0.943
##    75   6266       3    0.936 0.002969        0.931        0.942
##    76   6262       6    0.936 0.002989        0.930        0.941
##    77   6256       6    0.935 0.003008        0.929        0.941
##    78   6250       5    0.934 0.003024        0.928        0.940
##    79   6245       2    0.934 0.003031        0.928        0.940
##    80   6243       1    0.933 0.003034        0.928        0.939
##    81   6238       6    0.933 0.003053        0.927        0.939
##    82   6232       2    0.932 0.003060        0.926        0.938
##    83   6230       3    0.932 0.003069        0.926        0.938
##    84   6226       5    0.931 0.003085        0.925        0.937
##    85   6217       2    0.931 0.003091        0.925        0.937
##    86   6215       7    0.930 0.003113        0.924        0.936
##    87   6207       3    0.929 0.003122        0.923        0.935
##    88   6201       1    0.929 0.003125        0.923        0.935
##    89   6197       1    0.929 0.003128        0.923        0.935
##    90   6196       3    0.929 0.003138        0.922        0.935
##    91   6193       4    0.928 0.003150        0.922        0.934
##    92   6189       2    0.928 0.003156        0.921        0.934
##    93   6187       3    0.927 0.003165        0.921        0.933
##    94   6183       3    0.927 0.003174        0.921        0.933
##    95   6179       3    0.926 0.003183        0.920        0.933
##    96   6172       3    0.926 0.003192        0.920        0.932
##    97   6169       3    0.925 0.003201        0.919        0.932
##    98   6163       6    0.924 0.003219        0.918        0.931
##    99   6156       5    0.924 0.003234        0.917        0.930
##   101   6149       4    0.923 0.003246        0.917        0.930
##   102   6144       3    0.923 0.003255        0.916        0.929
##   103   6139       3    0.922 0.003264        0.916        0.929
##   104   6135       3    0.922 0.003272        0.915        0.928
##   105   6130       4    0.921 0.003284        0.915        0.928
##   106   6125       3    0.921 0.003293        0.914        0.927
##   107   6121       5    0.920 0.003307        0.914        0.926
##   108   6115       1    0.920 0.003310        0.913        0.926
##   109   6114       3    0.919 0.003319        0.913        0.926
##   110   6109       5    0.919 0.003333        0.912        0.925
##   111   6099       6    0.918 0.003350        0.911        0.924
##   112   6092       4    0.917 0.003361        0.911        0.924
##   113   6086       3    0.917 0.003370        0.910        0.923
##   114   6083       1    0.917 0.003373        0.910        0.923
##   115   6077       4    0.916 0.003384        0.909        0.923
##   116   6071       3    0.915 0.003392        0.909        0.922
##   117   6067       4    0.915 0.003403        0.908        0.922
##   118   6062       2    0.915 0.003409        0.908        0.921
##   119   6056       7    0.913 0.003428        0.907        0.920
##   120   6045       7    0.912 0.003448        0.906        0.919
##   121   6038       2    0.912 0.003453        0.905        0.919
##   122   6035       4    0.912 0.003464        0.905        0.918
##   123   6031       5    0.911 0.003478        0.904        0.918
##   124   6026       3    0.910 0.003486        0.904        0.917
##   125   6022       5    0.910 0.003499        0.903        0.916
##   126   6016       5    0.909 0.003513        0.902        0.916
##   127   6008       1    0.909 0.003515        0.902        0.916
##   128   6006       2    0.908 0.003521        0.901        0.915
##   129   6001       5    0.908 0.003534        0.901        0.915
##   130   5996       2    0.907 0.003539        0.900        0.914
##   131   5993       3    0.907 0.003547        0.900        0.914
##   132   5990       1    0.907 0.003550        0.900        0.914
##   133   5989       1    0.907 0.003552        0.900        0.914
##   134   5987       5    0.906 0.003565        0.899        0.913
##   135   5978       2    0.905 0.003571        0.898        0.912
##   136   5975       3    0.905 0.003579        0.898        0.912
##   137   5972       1    0.905 0.003581        0.898        0.912
##   138   5969       2    0.905 0.003586        0.898        0.912
##   139   5965       3    0.904 0.003594        0.897        0.911
##   140   5960       4    0.903 0.003605        0.896        0.911
##   141   5956       2    0.903 0.003610        0.896        0.910
##   142   5953       2    0.903 0.003615        0.896        0.910
##   143   5948       2    0.903 0.003620        0.896        0.910
##   144   5944       1    0.902 0.003623        0.895        0.910
##   145   5943       3    0.902 0.003630        0.895        0.909
##   146   5940       5    0.901 0.003643        0.894        0.908
##   147   5935       4    0.901 0.003653        0.893        0.908
##   148   5929       5    0.900 0.003666        0.893        0.907
##   149   5924       2    0.900 0.003671        0.892        0.907
##   150   5917       2    0.899 0.003676        0.892        0.906
##   151   5914       3    0.899 0.003684        0.892        0.906
##   153   5906       5    0.898 0.003696        0.891        0.905
##   154   5900       5    0.897 0.003709        0.890        0.905
##   155   5892       5    0.897 0.003721        0.889        0.904
##   156   5882       1    0.896 0.003724        0.889        0.904
##   157   5880       4    0.896 0.003734        0.888        0.903
##   158   5876       2    0.895 0.003738        0.888        0.903
##   159   5873       5    0.895 0.003751        0.887        0.902
##   160   5867       2    0.894 0.003756        0.887        0.902
##   161   5863       5    0.894 0.003768        0.886        0.901
##   163   5856       5    0.893 0.003780        0.885        0.900
##   164   5849       1    0.893 0.003783        0.885        0.900
##   165   5848       1    0.893 0.003785        0.885        0.900
##   166   5847       1    0.892 0.003787        0.885        0.900
##   167   5845       1    0.892 0.003790        0.885        0.900
##   168   5841       5    0.891 0.003802        0.884        0.899
##   169   5834       1    0.891 0.003804        0.884        0.899
##   170   5833       2    0.891 0.003809        0.884        0.899
##   171   5829       3    0.891 0.003817        0.883        0.898
##   172   5825       2    0.890 0.003821        0.883        0.898
##   173   5822       5    0.889 0.003833        0.882        0.897
##   174   5816       5    0.889 0.003845        0.881        0.896
##   175   5809       3    0.888 0.003852        0.881        0.896
##   176   5805       7    0.887 0.003869        0.880        0.895
##   178   5798       3    0.887 0.003876        0.879        0.894
##   179   5793       2    0.886 0.003881        0.879        0.894
##   180   5790       1    0.886 0.003883        0.879        0.894
##   181   5789       3    0.886 0.003890        0.878        0.893
##   182   5786       4    0.885 0.003899        0.878        0.893
##   183   5780       4    0.885 0.003909        0.877        0.892
##   185   5774       7    0.884 0.003925        0.876        0.891
##   186   5766       2    0.883 0.003930        0.876        0.891
##   187   5762       2    0.883 0.003934        0.875        0.891
##   188   5757       5    0.882 0.003946        0.874        0.890
##   189   5751       3    0.882 0.003953        0.874        0.889
##   190   5745       2    0.881 0.003957        0.874        0.889
##   191   5741       5    0.881 0.003969        0.873        0.888
##   192   5735       3    0.880 0.003975        0.872        0.888
##   193   5732       3    0.880 0.003982        0.872        0.888
##   194   5726       1    0.880 0.003984        0.872        0.887
##   195   5724       3    0.879 0.003991        0.871        0.887
##   196   5719       4    0.878 0.004000        0.871        0.886
##   197   5714       3    0.878 0.004007        0.870        0.886
##   200   5710       4    0.877 0.004016        0.870        0.885
##   201   5706       2    0.877 0.004020        0.869        0.885
##   202   5703       1    0.877 0.004023        0.869        0.885
##   203   5700       3    0.876 0.004029        0.869        0.884
##   204   5697       4    0.876 0.004038        0.868        0.884
##   205   5692       1    0.876 0.004041        0.868        0.884
##   206   5689       3    0.875 0.004047        0.867        0.883
##   208   5683       1    0.875 0.004049        0.867        0.883
##   209   5679       4    0.874 0.004058        0.867        0.882
##   210   5672       1    0.874 0.004060        0.866        0.882
##   211   5671       5    0.874 0.004072        0.866        0.882
##   212   5664       5    0.873 0.004082        0.865        0.881
##   213   5658       5    0.872 0.004093        0.864        0.880
##   214   5651       2    0.872 0.004098        0.864        0.880
##   216   5646       2    0.871 0.004102        0.863        0.879
##   217   5644       2    0.871 0.004106        0.863        0.879
##   218   5640       1    0.871 0.004109        0.863        0.879
##   219   5639       2    0.871 0.004113        0.863        0.879
##   220   5637       1    0.870 0.004115        0.862        0.879
##   221   5636       4    0.870 0.004124        0.862        0.878
##   222   5631       1    0.870 0.004126        0.862        0.878
##   223   5630       2    0.869 0.004130        0.861        0.877
##   224   5628       4    0.869 0.004139        0.861        0.877
##   225   5624       1    0.869 0.004141        0.861        0.877
##   226   5622       3    0.868 0.004147        0.860        0.876
##   227   5619       1    0.868 0.004150        0.860        0.876
##   228   5618       5    0.867 0.004160        0.859        0.875
##   229   5611       2    0.867 0.004165        0.859        0.875
##   230   5606       4    0.866 0.004173        0.858        0.874
##   231   5601       3    0.866 0.004179        0.858        0.874
##   232   5597       3    0.865 0.004186        0.857        0.874
##   233   5592       4    0.865 0.004194        0.857        0.873
##   234   5588       6    0.864 0.004207        0.856        0.872
##   236   5582       2    0.863 0.004211        0.855        0.872
##   237   5579       1    0.863 0.004213        0.855        0.872
##   238   5578       3    0.863 0.004219        0.855        0.871
##   239   5573       3    0.862 0.004226        0.854        0.871
##   240   5570       1    0.862 0.004228        0.854        0.871
##   241   5568       4    0.862 0.004236        0.853        0.870
##   242   5564       1    0.861 0.004238        0.853        0.870
##   243   5562       1    0.861 0.004240        0.853        0.870
##   244   5561       3    0.861 0.004246        0.853        0.869
##   245   5554       4    0.860 0.004254        0.852        0.869
##   246   5550       4    0.860 0.004263        0.851        0.868
##   247   5546       4    0.859 0.004271        0.851        0.867
##   248   5540       3    0.859 0.004277        0.850        0.867
##   249   5534       3    0.858 0.004283        0.850        0.866
##   250   5531       3    0.858 0.004289        0.849        0.866
##   251   5525       3    0.857 0.004295        0.849        0.866
##   252   5521       4    0.857 0.004303        0.848        0.865
##   253   5517       1    0.856 0.004305        0.848        0.865
##   254   5514       1    0.856 0.004307        0.848        0.865
##   255   5512       1    0.856 0.004309        0.848        0.865
##   256   5511       2    0.856 0.004313        0.847        0.864
##   257   5508       3    0.855 0.004320        0.847        0.864
##   258   5505       4    0.855 0.004328        0.846        0.863
##   259   5501       4    0.854 0.004336        0.846        0.863
##   261   5494       1    0.854 0.004338        0.845        0.862
##   263   5490       2    0.854 0.004342        0.845        0.862
##   264   5485       1    0.853 0.004344        0.845        0.862
##   265   5481       2    0.853 0.004347        0.845        0.862
##   266   5478       4    0.852 0.004355        0.844        0.861
##   267   5474       1    0.852 0.004357        0.844        0.861
##   268   5473       5    0.852 0.004367        0.843        0.860
##   269   5468       4    0.851 0.004375        0.842        0.860
##   270   5461       2    0.851 0.004379        0.842        0.859
##   271   5456       1    0.850 0.004381        0.842        0.859
##   272   5454       1    0.850 0.004383        0.842        0.859
##   273   5452       3    0.850 0.004389        0.841        0.858
##   274   5449       4    0.849 0.004397        0.841        0.858
##   275   5445       4    0.849 0.004405        0.840        0.857
##   276   5440       8    0.847 0.004420        0.839        0.856
##   277   5431       1    0.847 0.004422        0.839        0.856
##   278   5430       1    0.847 0.004424        0.838        0.856
##   280   5427       3    0.847 0.004430        0.838        0.855
##   281   5423       1    0.846 0.004432        0.838        0.855
##   282   5421       3    0.846 0.004438        0.837        0.855
##   283   5418       5    0.845 0.004447        0.836        0.854
##   284   5413       2    0.845 0.004451        0.836        0.854
##   285   5411       4    0.844 0.004459        0.836        0.853
##   286   5407       6    0.843 0.004470        0.835        0.852
##   288   5396       4    0.843 0.004478        0.834        0.851
##   289   5391       2    0.842 0.004482        0.834        0.851
##   290   5388       1    0.842 0.004483        0.833        0.851
##   291   5387       3    0.842 0.004489        0.833        0.851
##   292   5383       1    0.842 0.004491        0.833        0.850
##   293   5381       2    0.841 0.004495        0.832        0.850
##   294   5379       2    0.841 0.004499        0.832        0.850
##   295   5375       1    0.841 0.004500        0.832        0.850
##   296   5373       2    0.840 0.004504        0.832        0.849
##   298   5369       1    0.840 0.004506        0.832        0.849
##   299   5366       1    0.840 0.004508        0.831        0.849
##   300   5364       2    0.840 0.004512        0.831        0.849
##   302   5360       2    0.840 0.004516        0.831        0.848
##   303   5357       2    0.839 0.004519        0.830        0.848
##   304   5355       3    0.839 0.004525        0.830        0.848
##   305   5350       4    0.838 0.004532        0.829        0.847
##   306   5344       3    0.838 0.004538        0.829        0.847
##   307   5341       3    0.837 0.004544        0.828        0.846
##   308   5335       1    0.837 0.004545        0.828        0.846
##   309   5332       1    0.837 0.004547        0.828        0.846
##   310   5330       1    0.837 0.004549        0.828        0.846
##   312   5327       1    0.837 0.004551        0.828        0.845
##   313   5326       1    0.836 0.004553        0.827        0.845
##   314   5325       1    0.836 0.004555        0.827        0.845
##   315   5324       5    0.835 0.004564        0.827        0.844
##   317   5317       1    0.835 0.004566        0.826        0.844
##   318   5315       5    0.834 0.004575        0.826        0.843
##   319   5309       4    0.834 0.004582        0.825        0.843
##   320   5303       4    0.833 0.004590        0.824        0.842
##   321   5298       1    0.833 0.004591        0.824        0.842
##   322   5297       1    0.833 0.004593        0.824        0.842
##   323   5296       3    0.832 0.004599        0.823        0.842
##   325   5288       2    0.832 0.004602        0.823        0.841
##   326   5286       1    0.832 0.004604        0.823        0.841
##   327   5285       5    0.831 0.004613        0.822        0.840
##   328   5278       1    0.831 0.004615        0.822        0.840
##   329   5274       4    0.830 0.004622        0.821        0.840
##   330   5269       5    0.830 0.004631        0.821        0.839
##   333   5262       2    0.829 0.004635        0.820        0.838
##   334   5260       2    0.829 0.004639        0.820        0.838
##   335   5258       1    0.829 0.004640        0.820        0.838
##   336   5255       2    0.829 0.004644        0.819        0.838
##   337   5250       3    0.828 0.004649        0.819        0.837
##   338   5247       2    0.828 0.004653        0.819        0.837
##   339   5243       3    0.827 0.004658        0.818        0.836
##   340   5240       1    0.827 0.004660        0.818        0.836
##   341   5237       2    0.827 0.004664        0.818        0.836
##   342   5233       3    0.826 0.004669        0.817        0.835
##   343   5230       1    0.826 0.004671        0.817        0.835
##   344   5228       2    0.826 0.004674        0.817        0.835
##   345   5225       3    0.825 0.004680        0.816        0.835
##   346   5220       2    0.825 0.004683        0.816        0.834
##   349   5214       1    0.825 0.004685        0.816        0.834
##   350   5213       1    0.825 0.004687        0.816        0.834
##   351   5212       3    0.824 0.004692        0.815        0.833
##   352   5207       2    0.824 0.004696        0.815        0.833
##   353   5204       2    0.824 0.004699        0.814        0.833
##   354   5202       3    0.823 0.004704        0.814        0.832
##   355   5198       1    0.823 0.004706        0.814        0.832
##   356   5197       3    0.822 0.004711        0.813        0.832
##   357   5193       4    0.822 0.004718        0.813        0.831
##   359   5187       1    0.822 0.004720        0.813        0.831
##   360   5185       1    0.822 0.004722        0.812        0.831
##   361   5183       3    0.821 0.004727        0.812        0.830
##   362   5179       2    0.821 0.004731        0.812        0.830
##   363   5176       2    0.820 0.004734        0.811        0.830
##   364   5172       3    0.820 0.004739        0.811        0.829
##   365   5169       1    0.820 0.004741        0.811        0.829
##   366   5168       4    0.819 0.004748        0.810        0.829
##   368   5161       1    0.819 0.004750        0.810        0.828
##   369   5159       2    0.819 0.004753        0.809        0.828
##   370   5155       3    0.818 0.004758        0.809        0.828
##   371   5152       4    0.818 0.004765        0.808        0.827
##   372   5147       3    0.817 0.004770        0.808        0.827
##   374   5140       1    0.817 0.004772        0.808        0.826
##   375   5137       1    0.817 0.004774        0.807        0.826
##   376   5136       1    0.817 0.004776        0.807        0.826
##   379   5134       2    0.816 0.004779        0.807        0.826
##   380   5131       2    0.816 0.004782        0.807        0.825
##   381   5128       2    0.816 0.004786        0.806        0.825
##   382   5126       1    0.816 0.004788        0.806        0.825
##   383   5125       1    0.815 0.004789        0.806        0.825
##   384   5123       2    0.815 0.004793        0.806        0.824
##   385   5119       3    0.815 0.004798        0.805        0.824
##   386   5114       2    0.814 0.004801        0.805        0.824
##   387   5112       3    0.814 0.004806        0.804        0.823
##   388   5109       3    0.813 0.004811        0.804        0.823
##   390   5101       3    0.813 0.004817        0.803        0.822
##   391   5097       2    0.812 0.004820        0.803        0.822
##   392   5093       5    0.812 0.004828        0.802        0.821
##   393   5087       2    0.811 0.004832        0.802        0.821
##   394   5085       4    0.811 0.004838        0.801        0.820
##   395   5081       4    0.810 0.004845        0.801        0.820
##   396   5077       2    0.810 0.004849        0.800        0.819
##   397   5074       2    0.809 0.004852        0.800        0.819
##   398   5070       2    0.809 0.004855        0.800        0.819
##   399   5068       1    0.809 0.004857        0.800        0.819
##   400   5067       1    0.809 0.004859        0.799        0.818
##   401   5064       1    0.809 0.004860        0.799        0.818
##   404   5060       1    0.808 0.004862        0.799        0.818
##   405   5058       3    0.808 0.004867        0.799        0.818
##   406   5054       3    0.808 0.004872        0.798        0.817
##   407   5050       2    0.807 0.004875        0.798        0.817
##   408   5047       2    0.807 0.004878        0.797        0.817
##   410   5043       4    0.806 0.004885        0.797        0.816
##   412   5035       3    0.806 0.004890        0.796        0.815
##   413   5032       2    0.805 0.004893        0.796        0.815
##   414   5028       1    0.805 0.004895        0.796        0.815
##   415   5026       2    0.805 0.004898        0.795        0.815
##   416   5022       5    0.804 0.004907        0.795        0.814
##   418   5013       3    0.804 0.004911        0.794        0.813
##   419   5010       3    0.803 0.004916        0.794        0.813
##   421   5006       1    0.803 0.004918        0.793        0.813
##   422   5005       2    0.803 0.004921        0.793        0.812
##   425   5001       3    0.802 0.004926        0.793        0.812
##   426   4996       2    0.802 0.004929        0.792        0.812
##   427   4993       2    0.802 0.004933        0.792        0.811
##   430   4990       1    0.801 0.004934        0.792        0.811
##   431   4988       2    0.801 0.004938        0.792        0.811
##   432   4985       1    0.801 0.004939        0.791        0.811
##   433   4984       2    0.801 0.004942        0.791        0.810
##   434   4981       1    0.800 0.004944        0.791        0.810
##   435   4979       1    0.800 0.004946        0.791        0.810
##   438   4978       2    0.800 0.004949        0.790        0.810
##   439   4975       1    0.800 0.004950        0.790        0.810
##   441   4971       2    0.800 0.004954        0.790        0.809
##   442   4968       3    0.799 0.004959        0.789        0.809
##   443   4964       2    0.799 0.004962        0.789        0.808
##   444   4958       3    0.798 0.004967        0.789        0.808
##   445   4955       2    0.798 0.004970        0.788        0.808
##   447   4951       2    0.798 0.004973        0.788        0.807
##   448   4947       1    0.797 0.004975        0.788        0.807
##   449   4945       1    0.797 0.004976        0.788        0.807
##   450   4944       1    0.797 0.004978        0.787        0.807
##   452   4943       1    0.797 0.004979        0.787        0.807
##   453   4942       2    0.797 0.004983        0.787        0.806
##   454   4940       3    0.796 0.004987        0.786        0.806
##   455   4936       1    0.796 0.004989        0.786        0.806
##   456   4935       1    0.796 0.004991        0.786        0.806
##   457   4933       2    0.795 0.004994        0.786        0.805
##   458   4930       1    0.795 0.004995        0.786        0.805
##   460   4929       1    0.795 0.004997        0.785        0.805
##   461   4927       1    0.795 0.004999        0.785        0.805
##   462   4925       2    0.795 0.005002        0.785        0.805
##   463   4922       3    0.794 0.005007        0.784        0.804
##   464   4916       1    0.794 0.005008        0.784        0.804
##   468   4915       2    0.794 0.005011        0.784        0.804
##   469   4913       1    0.794 0.005013        0.784        0.803
##   470   4912       1    0.793 0.005015        0.784        0.803
##   471   4911       2    0.793 0.005018        0.783        0.803
##   472   4909       4    0.792 0.005024        0.783        0.802
##   473   4904       1    0.792 0.005026        0.782        0.802
##   474   4901       2    0.792 0.005029        0.782        0.802
##   476   4895       3    0.791 0.005033        0.782        0.801
##   477   4891       2    0.791 0.005037        0.781        0.801
##   478   4889       2    0.791 0.005040        0.781        0.801
##   479   4886       1    0.791 0.005041        0.781        0.801
##   480   4885       4    0.790 0.005048        0.780        0.800
##   481   4881       2    0.790 0.005051        0.780        0.800
##   483   4878       1    0.790 0.005052        0.780        0.799
##   484   4877       3    0.789 0.005057        0.779        0.799
##   485   4874       1    0.789 0.005058        0.779        0.799
##   486   4873       1    0.789 0.005060        0.779        0.799
##   487   4871       2    0.788 0.005063        0.779        0.798
##   488   4869       2    0.788 0.005066        0.778        0.798
##   490   4866       2    0.788 0.005069        0.778        0.798
##   491   4863       4    0.787 0.005075        0.777        0.797
##   492   4858       2    0.787 0.005079        0.777        0.797
##   493   4856       2    0.786 0.005082        0.777        0.796
##   494   4850       7    0.785 0.005092        0.775        0.795
##   495   4843       1    0.785 0.005094        0.775        0.795
##   496   4841       1    0.785 0.005095        0.775        0.795
##   497   4840       1    0.785 0.005097        0.775        0.795
##   498   4838       1    0.785 0.005098        0.775        0.795
##   499   4837       1    0.784 0.005100        0.775        0.795
##   501   4836       1    0.784 0.005101        0.774        0.794
##   502   4835       2    0.784 0.005105        0.774        0.794
##   505   4831       2    0.784 0.005108        0.774        0.794
##   507   4829       2    0.783 0.005111        0.773        0.793
##   508   4826       1    0.783 0.005112        0.773        0.793
##   509   4823       1    0.783 0.005114        0.773        0.793
##   510   4821       1    0.783 0.005115        0.773        0.793
##   511   4819       2    0.783 0.005118        0.773        0.793
##   514   4813       1    0.782 0.005120        0.772        0.792
##   515   4812       3    0.782 0.005124        0.772        0.792
##   516   4807       5    0.781 0.005132        0.771        0.791
##   517   4801       1    0.781 0.005133        0.771        0.791
##   518   4800       3    0.780 0.005138        0.770        0.791
##   519   4796       1    0.780 0.005139        0.770        0.790
##   520   4795       3    0.780 0.005144        0.770        0.790
##   523   4788       1    0.780 0.005145        0.770        0.790
##   524   4786       2    0.779 0.005148        0.769        0.789
##   525   4784       1    0.779 0.005150        0.769        0.789
##   526   4782       1    0.779 0.005151        0.769        0.789
##   527   4780       3    0.778 0.005156        0.768        0.789
##   528   4774       1    0.778 0.005157        0.768        0.788
##   530   4772       1    0.778 0.005159        0.768        0.788
##   531   4771       1    0.778 0.005160        0.768        0.788
##   532   4770       1    0.778 0.005162        0.768        0.788
##   533   4765       2    0.777 0.005165        0.767        0.788
##   534   4763       2    0.777 0.005168        0.767        0.787
##   537   4760       2    0.777 0.005171        0.767        0.787
##   538   4756       2    0.777 0.005174        0.766        0.787
##   539   4751       1    0.776 0.005175        0.766        0.787
##   540   4750       4    0.776 0.005181        0.766        0.786
##   543   4742       1    0.776 0.005183        0.765        0.786
##   544   4739       1    0.775 0.005184        0.765        0.786
##   545   4735       1    0.775 0.005186        0.765        0.785
##   546   4731       1    0.775 0.005187        0.765        0.785
##   547   4730       2    0.775 0.005190        0.765        0.785
##   548   4727       1    0.775 0.005192        0.764        0.785
##   549   4726       2    0.774 0.005195        0.764        0.784
##   550   4722       2    0.774 0.005198        0.764        0.784
##   551   4720       1    0.774 0.005199        0.764        0.784
##   552   4719       2    0.773 0.005202        0.763        0.784
##   553   4716       1    0.773 0.005204        0.763        0.783
##   554   4711       1    0.773 0.005205        0.763        0.783
##   556   4709       4    0.772 0.005211        0.762        0.783
##   557   4704       2    0.772 0.005214        0.762        0.782
##   558   4702       2    0.772 0.005217        0.762        0.782
##   559   4700       1    0.772 0.005218        0.761        0.782
##   563   4696       1    0.771 0.005220        0.761        0.782
##   564   4695       2    0.771 0.005223        0.761        0.781
##   566   4691       1    0.771 0.005224        0.761        0.781
##   567   4690       3    0.770 0.005229        0.760        0.781
##   568   4687       2    0.770 0.005232        0.760        0.780
##   569   4684       1    0.770 0.005233        0.760        0.780
##   571   4683       3    0.769 0.005237        0.759        0.780
##   572   4679       2    0.769 0.005240        0.759        0.779
##   573   4677       2    0.769 0.005243        0.759        0.779
##   574   4675       2    0.768 0.005246        0.758        0.779
##   575   4673       1    0.768 0.005248        0.758        0.779
##   576   4671       2    0.768 0.005251        0.758        0.778
##   577   4668       3    0.767 0.005255        0.757        0.778
##   581   4659       5    0.767 0.005262        0.756        0.777
##   582   4652       3    0.766 0.005267        0.756        0.777
##   586   4648       1    0.766 0.005268        0.756        0.776
##   587   4647       3    0.766 0.005272        0.755        0.776
##   588   4643       3    0.765 0.005277        0.755        0.775
##   589   4639       3    0.765 0.005281        0.754        0.775
##   590   4635       1    0.764 0.005282        0.754        0.775
##   591   4633       1    0.764 0.005284        0.754        0.775
##   592   4632       2    0.764 0.005287        0.754        0.774
##   593   4630       1    0.764 0.005288        0.753        0.774
##   594   4628       1    0.764 0.005290        0.753        0.774
##   595   4627       2    0.763 0.005292        0.753        0.774
##   596   4624       4    0.763 0.005298        0.752        0.773
##   598   4617       3    0.762 0.005302        0.752        0.772
##   599   4613       4    0.761 0.005308        0.751        0.772
##   600   4607       2    0.761 0.005311        0.751        0.772
##   601   4604       2    0.761 0.005314        0.750        0.771
##   603   4599       1    0.761 0.005315        0.750        0.771
##   605   4597       2    0.760 0.005318        0.750        0.771
##   606   4594       1    0.760 0.005319        0.750        0.771
##   607   4593       1    0.760 0.005321        0.750        0.770
##   608   4591       2    0.760 0.005324        0.749        0.770
##   609   4589       2    0.759 0.005326        0.749        0.770
##   610   4586       2    0.759 0.005329        0.749        0.769
##   611   4583       1    0.759 0.005331        0.748        0.769
##   612   4582       1    0.759 0.005332        0.748        0.769
##   614   4579       1    0.758 0.005333        0.748        0.769
##   615   4577       2    0.758 0.005336        0.748        0.769
##   616   4573       2    0.758 0.005339        0.747        0.768
##   617   4571       2    0.757 0.005342        0.747        0.768
##   620   4569       1    0.757 0.005343        0.747        0.768
##   622   4567       3    0.757 0.005348        0.746        0.767
##   623   4563       3    0.756 0.005352        0.746        0.767
##   626   4559       3    0.756 0.005356        0.745        0.766
##   627   4556       1    0.756 0.005357        0.745        0.766
##   628   4552       2    0.755 0.005360        0.745        0.766
##   629   4550       2    0.755 0.005363        0.744        0.765
##   630   4546       2    0.755 0.005366        0.744        0.765
##   631   4544       2    0.754 0.005368        0.744        0.765
##   632   4539       2    0.754 0.005371        0.743        0.765
##   633   4537       2    0.754 0.005374        0.743        0.764
##   634   4534       2    0.753 0.005377        0.743        0.764
##   635   4532       2    0.753 0.005380        0.742        0.764
##   636   4529       1    0.753 0.005381        0.742        0.763
##   637   4524       1    0.753 0.005382        0.742        0.763
##   638   4523       1    0.752 0.005384        0.742        0.763
##   639   4519       1    0.752 0.005385        0.742        0.763
##   642   4517       2    0.752 0.005388        0.741        0.763
##   643   4515       1    0.752 0.005389        0.741        0.762
##   646   4509       3    0.751 0.005393        0.741        0.762
##   647   4506       2    0.751 0.005396        0.740        0.762
##   649   4501       1    0.751 0.005397        0.740        0.761
##   650   4500       1    0.751 0.005399        0.740        0.761
##   651   4497       3    0.750 0.005403        0.740        0.761
##   652   4493       1    0.750 0.005404        0.739        0.761
##   655   4491       3    0.749 0.005408        0.739        0.760
##   656   4487       1    0.749 0.005410        0.739        0.760
##   657   4486       1    0.749 0.005411        0.739        0.760
##   658   4485       5    0.748 0.005418        0.738        0.759
##   659   4480       3    0.748 0.005422        0.737        0.758
##   661   4475       2    0.747 0.005425        0.737        0.758
##   663   4473       2    0.747 0.005428        0.737        0.758
##   664   4469       3    0.747 0.005432        0.736        0.757
##   665   4465       4    0.746 0.005437        0.735        0.757
##   666   4461       2    0.746 0.005440        0.735        0.756
##   667   4458       2    0.745 0.005442        0.735        0.756
##   669   4456       2    0.745 0.005445        0.734        0.756
##   670   4452       2    0.745 0.005448        0.734        0.755
##   673   4449       2    0.744 0.005451        0.734        0.755
##   674   4447       1    0.744 0.005452        0.733        0.755
##   676   4442       3    0.744 0.005456        0.733        0.754
##   677   4439       3    0.743 0.005460        0.732        0.754
##   678   4435       1    0.743 0.005461        0.732        0.754
##   680   4432       1    0.743 0.005463        0.732        0.754
##   681   4431       2    0.742 0.005465        0.732        0.753
##   682   4426       1    0.742 0.005467        0.732        0.753
##   683   4425       2    0.742 0.005469        0.731        0.753
##   684   4423       1    0.742 0.005471        0.731        0.753
##   687   4422       2    0.741 0.005473        0.731        0.752
##   688   4420       2    0.741 0.005476        0.730        0.752
##   690   4417       2    0.741 0.005479        0.730        0.752
##   691   4415       1    0.741 0.005480        0.730        0.751
##   693   4409       1    0.740 0.005481        0.730        0.751
##   694   4406       3    0.740 0.005485        0.729        0.751
##   695   4400       3    0.739 0.005489        0.729        0.750
##   697   4396       1    0.739 0.005491        0.729        0.750
##   699   4395       2    0.739 0.005493        0.728        0.750
##   700   4392       2    0.739 0.005496        0.728        0.749
##   701   4389       3    0.738 0.005500        0.727        0.749
##   702   4384       3    0.738 0.005504        0.727        0.748
##   703   4381       1    0.737 0.005505        0.727        0.748
##   704   4380       4    0.737 0.005510        0.726        0.748
##   706   4375       1    0.737 0.005512        0.726        0.747
##   707   4374       2    0.736 0.005514        0.725        0.747
##   708   4371       2    0.736 0.005517        0.725        0.747
##   709   4368       2    0.736 0.005520        0.725        0.746
##   710   4365       4    0.735 0.005525        0.724        0.746
##   711   4361       1    0.735 0.005526        0.724        0.746
##   712   4358       2    0.734 0.005529        0.724        0.745
##   713   4356       3    0.734 0.005533        0.723        0.745
##   714   4352       1    0.734 0.005534        0.723        0.745
##   715   4347       2    0.733 0.005536        0.723        0.744
##   716   4345       1    0.733 0.005538        0.722        0.744
##   718   4343       2    0.733 0.005540        0.722        0.744
##   719   4339       1    0.733 0.005542        0.722        0.744
##   720   4338       3    0.732 0.005546        0.721        0.743
##   721   4333       1    0.732 0.005547        0.721        0.743
##   723   4330       2    0.732 0.005549        0.721        0.743
##   724   4326       1    0.731 0.005551        0.721        0.742
##   725   4324       2    0.731 0.005553        0.720        0.742
##   726   4320       1    0.731 0.005555        0.720        0.742
##   727   4319       1    0.731 0.005556        0.720        0.742
##   728   4318       3    0.730 0.005560        0.719        0.741
##   730   4314       1    0.730 0.005561        0.719        0.741
##   731   4311       2    0.730 0.005564        0.719        0.741
##   732   4307       1    0.730 0.005565        0.719        0.741
##   733   4306       1    0.729 0.005566        0.719        0.740
##   734   4305       3    0.729 0.005570        0.718        0.740
##   735   4302       2    0.729 0.005573        0.718        0.740
##   736   4299       1    0.728 0.005574        0.718        0.739
##   738   4297       1    0.728 0.005575        0.717        0.739
##   739   4295       1    0.728 0.005576        0.717        0.739
##   740   4294       1    0.728 0.005578        0.717        0.739
##   741   4293       2    0.728 0.005580        0.717        0.739
##   742   4290       1    0.727 0.005582        0.717        0.738
##   744   4286       2    0.727 0.005584        0.716        0.738
##   746   4283       1    0.727 0.005585        0.716        0.738
##   747   4282       1    0.727 0.005587        0.716        0.738
##   748   4281       2    0.726 0.005589        0.715        0.737
##   751   4277       2    0.726 0.005592        0.715        0.737
##   752   4275       2    0.726 0.005594        0.715        0.737
##   753   4272       1    0.726 0.005596        0.715        0.737
##   754   4271       2    0.725 0.005598        0.714        0.736
##   755   4269       2    0.725 0.005601        0.714        0.736
##   756   4264       1    0.725 0.005602        0.714        0.736
##   758   4262       2    0.724 0.005604        0.713        0.735
##   759   4258       2    0.724 0.005607        0.713        0.735
##   760   4255       2    0.724 0.005609        0.713        0.735
##   762   4253       1    0.723 0.005611        0.713        0.735
##   763   4251       2    0.723 0.005613        0.712        0.734
##   765   4248       1    0.723 0.005615        0.712        0.734
##   766   4247       1    0.723 0.005616        0.712        0.734
##   767   4246       1    0.723 0.005617        0.712        0.734
##   768   4244       3    0.722 0.005621        0.711        0.733
##   770   4240       1    0.722 0.005622        0.711        0.733
##   771   4239       1    0.722 0.005623        0.711        0.733
##   772   4238       3    0.721 0.005627        0.710        0.732
##   773   4235       3    0.721 0.005631        0.710        0.732
##   774   4232       1    0.721 0.005632        0.710        0.732
##   776   4230       1    0.720 0.005633        0.709        0.732
##   777   4228       1    0.720 0.005635        0.709        0.731
##   781   4222       1    0.720 0.005636        0.709        0.731
##   782   4219       1    0.720 0.005637        0.709        0.731
##   783   4218       2    0.720 0.005640        0.709        0.731
##   784   4215       1    0.719 0.005641        0.708        0.731
##   785   4213       2    0.719 0.005643        0.708        0.730
##   786   4211       1    0.719 0.005645        0.708        0.730
##   787   4209       1    0.719 0.005646        0.708        0.730
##   789   4206       2    0.718 0.005648        0.707        0.730
##   790   4202       2    0.718 0.005651        0.707        0.729
##   791   4198       1    0.718 0.005652        0.707        0.729
##   792   4197       3    0.717 0.005656        0.706        0.729
##   793   4193       4    0.717 0.005661        0.706        0.728
##   796   4186       2    0.716 0.005663        0.705        0.727
##   797   4184       2    0.716 0.005666        0.705        0.727
##   798   4182       3    0.715 0.005669        0.704        0.727
##   800   4177       1    0.715 0.005670        0.704        0.726
##   801   4176       3    0.715 0.005674        0.704        0.726
##   803   4169       1    0.715 0.005675        0.704        0.726
##   804   4168       2    0.714 0.005678        0.703        0.725
##   805   4163       2    0.714 0.005680        0.703        0.725
##   806   4158       3    0.713 0.005684        0.702        0.725
##   808   4154       2    0.713 0.005686        0.702        0.724
##   809   4151       1    0.713 0.005688        0.702        0.724
##   810   4149       1    0.713 0.005689        0.702        0.724
##   812   4147       2    0.712 0.005691        0.701        0.724
##   813   4145       1    0.712 0.005693        0.701        0.723
##   814   4144       2    0.712 0.005695        0.701        0.723
##   816   4140       1    0.712 0.005696        0.701        0.723
##   819   4137       1    0.712 0.005697        0.700        0.723
##   821   4134       1    0.711 0.005699        0.700        0.723
##   822   4131       1    0.711 0.005700        0.700        0.722
##   823   4129       2    0.711 0.005702        0.700        0.722
##   825   4124       3    0.710 0.005706        0.699        0.722
##   826   4121       2    0.710 0.005708        0.699        0.721
##   828   4118       2    0.710 0.005711        0.699        0.721
##   829   4116       2    0.709 0.005713        0.698        0.721
##   830   4114       1    0.709 0.005714        0.698        0.720
##   831   4113       3    0.709 0.005718        0.697        0.720
##   833   4110       2    0.708 0.005721        0.697        0.720
##   834   4108       1    0.708 0.005722        0.697        0.719
##   835   4107       2    0.708 0.005724        0.697        0.719
##   836   4104       6    0.707 0.005731        0.696        0.718
##   837   4098       1    0.707 0.005733        0.695        0.718
##   839   4096       2    0.706 0.005735        0.695        0.717
##   841   4089       2    0.706 0.005737        0.695        0.717
##   843   4084       2    0.705 0.005740        0.694        0.717
##   844   4082       2    0.705 0.005742        0.694        0.716
##   845   4080       1    0.705 0.005743        0.694        0.716
##   847   4079       2    0.705 0.005746        0.693        0.716
##   848   4076       1    0.704 0.005747        0.693        0.716
##   850   4073       2    0.704 0.005749        0.693        0.715
##   851   4071       1    0.704 0.005750        0.693        0.715
##   852   4069       1    0.704 0.005752        0.693        0.715
##   853   4064       2    0.703 0.005754        0.692        0.715
##   854   4062       1    0.703 0.005755        0.692        0.715
##   855   4058       4    0.703 0.005760        0.691        0.714
##   856   4054       1    0.702 0.005761        0.691        0.714
##   857   4050       2    0.702 0.005763        0.691        0.713
##   858   4047       2    0.702 0.005766        0.690        0.713
##   859   4045       3    0.701 0.005769        0.690        0.713
##   861   4039       1    0.701 0.005771        0.690        0.712
##   862   4038       1    0.701 0.005772        0.690        0.712
##   864   4036       1    0.701 0.005773        0.689        0.712
##   867   4032       1    0.700 0.005774        0.689        0.712
##   868   4019       4    0.700 0.005779        0.689        0.711
##   869   4014       2    0.699 0.005781        0.688        0.711
##   870   4011       1    0.699 0.005782        0.688        0.711
##   874   3975       2    0.699 0.005785        0.688        0.710
##   875   3970       2    0.699 0.005787        0.687        0.710
##   876   3967       1    0.698 0.005789        0.687        0.710
##   877   3966       1    0.698 0.005790        0.687        0.710
##   880   3937       2    0.698 0.005792        0.687        0.709
##   881   3926       1    0.698 0.005794        0.686        0.709
##   882   3919       2    0.697 0.005796        0.686        0.709
##   883   3916       2    0.697 0.005799        0.686        0.708
##   884   3914       1    0.697 0.005800        0.685        0.708
##   885   3909       3    0.696 0.005804        0.685        0.708
##   886   3902       1    0.696 0.005805        0.685        0.708
##   887   3895       1    0.696 0.005806        0.685        0.707
##   889   3881       2    0.696 0.005809        0.684        0.707
##   890   3879       2    0.695 0.005811        0.684        0.707
##   891   3877       1    0.695 0.005812        0.684        0.706
##   893   3861       1    0.695 0.005814        0.683        0.706
##   894   3857       1    0.695 0.005815        0.683        0.706
##   895   3851       1    0.694 0.005816        0.683        0.706
##   898   3841       2    0.694 0.005819        0.683        0.706
##   900   3829       2    0.694 0.005821        0.682        0.705
##   901   3826       1    0.694 0.005823        0.682        0.705
##   903   3813       2    0.693 0.005825        0.682        0.705
##   904   3809       1    0.693 0.005827        0.682        0.704
##   905   3808       1    0.693 0.005828        0.681        0.704
##   906   3803       1    0.693 0.005829        0.681        0.704
##   907   3798       1    0.692 0.005831        0.681        0.704
##   909   3786       2    0.692 0.005833        0.681        0.704
##   910   3784       2    0.692 0.005836        0.680        0.703
##   911   3782       4    0.691 0.005841        0.680        0.703
##   913   3776       2    0.691 0.005844        0.679        0.702
##   917   3757       1    0.690 0.005845        0.679        0.702
##   918   3755       1    0.690 0.005847        0.679        0.702
##   919   3753       1    0.690 0.005848        0.679        0.702
##   921   3749       4    0.689 0.005853        0.678        0.701
##   923   3734       1    0.689 0.005855        0.678        0.701
##   924   3727       1    0.689 0.005856        0.678        0.701
##   925   3726       1    0.689 0.005857        0.677        0.700
##   926   3725       2    0.688 0.005860        0.677        0.700
##   928   3715       1    0.688 0.005861        0.677        0.700
##   930   3699       2    0.688 0.005864        0.676        0.699
##   931   3692       2    0.687 0.005867        0.676        0.699
##   935   3681       1    0.687 0.005868        0.676        0.699
##   936   3676       1    0.687 0.005869        0.676        0.699
##   937   3673       2    0.687 0.005872        0.675        0.698
##   938   3668       2    0.686 0.005875        0.675        0.698
##   939   3666       2    0.686 0.005878        0.675        0.698
##   941   3657       1    0.686 0.005879        0.674        0.697
##   943   3640       2    0.685 0.005882        0.674        0.697
##   944   3630       3    0.685 0.005886        0.673        0.696
##   945   3627       1    0.685 0.005888        0.673        0.696
##   947   3625       2    0.684 0.005890        0.673        0.696
##   948   3621       1    0.684 0.005892        0.673        0.696
##   951   3596       1    0.684 0.005893        0.672        0.696
##   952   3592       2    0.683 0.005896        0.672        0.695
##   955   3581       2    0.683 0.005899        0.672        0.695
##   956   3578       2    0.683 0.005902        0.671        0.694
##   957   3571       1    0.683 0.005903        0.671        0.694
##   958   3569       3    0.682 0.005908        0.670        0.694
##   960   3560       1    0.682 0.005909        0.670        0.693
##   961   3559       2    0.681 0.005912        0.670        0.693
##   962   3552       1    0.681 0.005913        0.670        0.693
##   964   3538       1    0.681 0.005915        0.670        0.693
##   966   3529       2    0.681 0.005918        0.669        0.692
##   968   3524       2    0.680 0.005921        0.669        0.692
##   969   3515       1    0.680 0.005922        0.669        0.692
##   970   3508       1    0.680 0.005924        0.668        0.692
##   971   3500       2    0.679 0.005927        0.668        0.691
##   972   3493       2    0.679 0.005930        0.668        0.691
##   973   3486       1    0.679 0.005931        0.667        0.691
##   974   3484       1    0.679 0.005933        0.667        0.690
##   975   3483       1    0.678 0.005934        0.667        0.690
##   976   3476       1    0.678 0.005936        0.667        0.690
##   977   3469       1    0.678 0.005937        0.667        0.690
##   978   3464       1    0.678 0.005939        0.666        0.690
##   979   3462       1    0.678 0.005940        0.666        0.689
##   980   3455       1    0.678 0.005942        0.666        0.689
##   982   3452       2    0.677 0.005945        0.666        0.689
##   983   3445       1    0.677 0.005946        0.665        0.689
##   984   3438       1    0.677 0.005948        0.665        0.688
##   986   3422       1    0.677 0.005949        0.665        0.688
##   987   3415       1    0.676 0.005951        0.665        0.688
##   988   3413       1    0.676 0.005952        0.665        0.688
##   990   3404       1    0.676 0.005954        0.664        0.688
##   992   3393       2    0.676 0.005957        0.664        0.687
##   993   3384       1    0.675 0.005959        0.664        0.687
##   994   3382       1    0.675 0.005960        0.664        0.687
##   997   3378       1    0.675 0.005962        0.663        0.687
##   998   3374       1    0.675 0.005964        0.663        0.687
##   999   3368       1    0.675 0.005965        0.663        0.686
##  1000   3362       1    0.674 0.005967        0.663        0.686
##  1001   3353       1    0.674 0.005968        0.663        0.686
##  1002   3351       1    0.674 0.005970        0.662        0.686
##  1003   3350       2    0.674 0.005973        0.662        0.685
##  1005   3336       1    0.673 0.005975        0.662        0.685
##  1006   3331       2    0.673 0.005978        0.661        0.685
##  1007   3319       1    0.673 0.005980        0.661        0.685
##  1008   3312       1    0.673 0.005981        0.661        0.684
##  1010   3311       2    0.672 0.005985        0.660        0.684
##  1013   3289       3    0.671 0.005990        0.660        0.683
##  1014   3283       1    0.671 0.005991        0.660        0.683
##  1015   3280       1    0.671 0.005993        0.659        0.683
##  1016   3279       1    0.671 0.005995        0.659        0.683
##  1021   3255       2    0.670 0.005998        0.659        0.682
##  1024   3251       1    0.670 0.006000        0.659        0.682
##  1025   3248       1    0.670 0.006001        0.658        0.682
##  1026   3243       1    0.670 0.006003        0.658        0.682
##  1027   3238       3    0.669 0.006008        0.658        0.681
##  1029   3227       1    0.669 0.006010        0.657        0.681
##  1031   3224       4    0.668 0.006017        0.657        0.680
##  1032   3214       1    0.668 0.006019        0.656        0.680
##  1034   3200       1    0.668 0.006020        0.656        0.680
##  1036   3187       2    0.667 0.006024        0.656        0.679
##  1037   3184       1    0.667 0.006026        0.655        0.679
##  1040   3176       2    0.667 0.006029        0.655        0.679
##  1041   3167       1    0.667 0.006031        0.655        0.678
##  1042   3159       3    0.666 0.006036        0.654        0.678
##  1043   3147       2    0.665 0.006040        0.654        0.677
##  1045   3145       1    0.665 0.006041        0.654        0.677
##  1047   3128       1    0.665 0.006043        0.653        0.677
##  1052   3117       2    0.665 0.006047        0.653        0.677
##  1055   3092       2    0.664 0.006051        0.652        0.676
##  1057   3077       1    0.664 0.006053        0.652        0.676
##  1063   3059       1    0.664 0.006054        0.652        0.676
##  1066   3056       1    0.664 0.006056        0.652        0.676
##  1067   3050       2    0.663 0.006060        0.651        0.675
##  1072   3018       1    0.663 0.006062        0.651        0.675
##  1074   3011       4    0.662 0.006070        0.650        0.674
##  1077   2984       1    0.662 0.006072        0.650        0.674
##  1079   2983       1    0.662 0.006074        0.650        0.674
##  1081   2973       1    0.661 0.006076        0.650        0.673
##  1083   2965       1    0.661 0.006078        0.649        0.673
##  1084   2955       4    0.660 0.006086        0.648        0.672
##  1086   2948       2    0.660 0.006091        0.648        0.672
##  1088   2945       2    0.659 0.006095        0.647        0.671
##  1090   2930       1    0.659 0.006097        0.647        0.671
##  1091   2925       1    0.659 0.006099        0.647        0.671
##  1093   2920       1    0.659 0.006101        0.647        0.671
##  1094   2919       1    0.658 0.006103        0.647        0.670
##  1101   2910       1    0.658 0.006105        0.646        0.670
##  1102   2909       1    0.658 0.006107        0.646        0.670
##  1106   2888       2    0.658 0.006111        0.646        0.670
##  1107   2886       1    0.657 0.006114        0.645        0.669
##  1108   2885       1    0.657 0.006116        0.645        0.669
##  1109   2876       1    0.657 0.006118        0.645        0.669
##  1110   2872       1    0.657 0.006120        0.645        0.669
##  1111   2865       1    0.656 0.006122        0.644        0.668
##  1112   2859       1    0.656 0.006124        0.644        0.668
##  1113   2847       1    0.656 0.006126        0.644        0.668
##  1114   2845       1    0.656 0.006129        0.644        0.668
##  1115   2844       1    0.655 0.006131        0.644        0.668
##  1117   2835       1    0.655 0.006133        0.643        0.667
##  1118   2827       1    0.655 0.006135        0.643        0.667
##  1119   2819       2    0.655 0.006140        0.643        0.667
##  1120   2812       1    0.654 0.006142        0.642        0.666
##  1122   2810       1    0.654 0.006144        0.642        0.666
##  1124   2795       1    0.654 0.006146        0.642        0.666
##  1126   2782       1    0.654 0.006149        0.642        0.666
##  1129   2773       1    0.653 0.006151        0.641        0.666
##  1130   2766       2    0.653 0.006156        0.641        0.665
##  1132   2758       1    0.653 0.006158        0.641        0.665
##  1134   2741       1    0.652 0.006160        0.640        0.665
##  1135   2740       2    0.652 0.006165        0.640        0.664
##  1136   2738       1    0.652 0.006167        0.640        0.664
##  1138   2723       1    0.651 0.006170        0.639        0.664
##  1141   2711       2    0.651 0.006174        0.639        0.663
##  1142   2709       2    0.650 0.006179        0.638        0.663
##  1143   2707       1    0.650 0.006182        0.638        0.662
##  1146   2691       1    0.650 0.006184        0.638        0.662
##  1147   2683       1    0.650 0.006186        0.638        0.662
##  1149   2674       1    0.650 0.006189        0.637        0.662
##  1153   2647       3    0.649 0.006197        0.637        0.661
##  1154   2639       1    0.649 0.006199        0.636        0.661
##  1155   2624       2    0.648 0.006204        0.636        0.660
##  1156   2621       2    0.648 0.006209        0.635        0.660
##  1158   2616       1    0.647 0.006212        0.635        0.660
##  1159   2612       1    0.647 0.006214        0.635        0.659
##  1160   2605       1    0.647 0.006217        0.635        0.659
##  1161   2595       1    0.647 0.006220        0.634        0.659
##  1163   2588       1    0.646 0.006222        0.634        0.659
##  1166   2578       2    0.646 0.006227        0.634        0.658
##  1168   2558       1    0.646 0.006230        0.633        0.658
##  1175   2529       1    0.645 0.006233        0.633        0.658
##  1176   2528       1    0.645 0.006236        0.633        0.657
##  1178   2525       2    0.645 0.006241        0.632        0.657
##  1179   2517       1    0.644 0.006244        0.632        0.657
##  1181   2506       1    0.644 0.006247        0.632        0.656
##  1186   2486       1    0.644 0.006250        0.632        0.656
##  1187   2476       2    0.643 0.006255        0.631        0.656
##  1188   2464       1    0.643 0.006258        0.631        0.655
##  1189   2454       1    0.643 0.006261        0.631        0.655
##  1190   2450       1    0.642 0.006264        0.630        0.655
##  1191   2449       1    0.642 0.006267        0.630        0.655
##  1193   2442       1    0.642 0.006270        0.630        0.654
##  1194   2433       1    0.642 0.006273        0.629        0.654
##  1197   2409       2    0.641 0.006279        0.629        0.654
##  1200   2400       1    0.641 0.006282        0.629        0.653
##  1202   2379       1    0.641 0.006285        0.628        0.653
##  1206   2360       2    0.640 0.006292        0.628        0.652
##  1207   2352       1    0.640 0.006295        0.628        0.652
##  1209   2337       1    0.640 0.006298        0.627        0.652
##  1211   2331       1    0.639 0.006301        0.627        0.652
##  1212   2330       1    0.639 0.006305        0.627        0.651
##  1213   2328       1    0.639 0.006308        0.626        0.651
##  1214   2322       1    0.638 0.006311        0.626        0.651
##  1216   2308       2    0.638 0.006318        0.626        0.650
##  1217   2299       1    0.638 0.006321        0.625        0.650
##  1218   2293       2    0.637 0.006328        0.625        0.650
##  1224   2276       1    0.637 0.006331        0.624        0.649
##  1227   2271       1    0.636 0.006335        0.624        0.649
##  1228   2262       1    0.636 0.006338        0.624        0.649
##  1230   2252       1    0.636 0.006342        0.624        0.648
##  1231   2248       1    0.636 0.006345        0.623        0.648
##  1234   2242       1    0.635 0.006349        0.623        0.648
##  1235   2233       2    0.635 0.006356        0.622        0.647
##  1240   2217       1    0.634 0.006359        0.622        0.647
##  1241   2215       2    0.634 0.006366        0.622        0.646
##  1242   2211       1    0.634 0.006370        0.621        0.646
##  1243   2205       1    0.633 0.006374        0.621        0.646
##  1245   2200       1    0.633 0.006377        0.621        0.646
##  1246   2196       1    0.633 0.006381        0.620        0.645
##  1247   2195       1    0.632 0.006384        0.620        0.645
##  1253   2172       1    0.632 0.006388        0.620        0.645
##  1261   2145       1    0.632 0.006392        0.619        0.645
##  1264   2135       1    0.632 0.006396        0.619        0.644
##  1267   2121       1    0.631 0.006400        0.619        0.644
##  1268   2120       1    0.631 0.006404        0.619        0.644
##  1271   2112       1    0.631 0.006407        0.618        0.643
##  1273   2096       1    0.630 0.006411        0.618        0.643
##  1275   2082       1    0.630 0.006416        0.618        0.643
##  1276   2081       1    0.630 0.006420        0.617        0.642
##  1277   2079       1    0.629 0.006424        0.617        0.642
##  1279   2070       1    0.629 0.006428        0.617        0.642
##  1283   2056       1    0.629 0.006432        0.616        0.642
##  1284   2053       2    0.628 0.006440        0.616        0.641
##  1285   2048       2    0.628 0.006449        0.615        0.640
##  1291   2021       1    0.627 0.006453        0.615        0.640
##  1292   2015       1    0.627 0.006457        0.614        0.640
##  1293   2007       1    0.627 0.006461        0.614        0.639
##  1300   1968       1    0.626 0.006466        0.614        0.639
##  1302   1949       2    0.626 0.006475        0.613        0.639
##  1303   1947       1    0.625 0.006480        0.613        0.638
##  1306   1936       1    0.625 0.006485        0.613        0.638
##  1310   1917       1    0.625 0.006489        0.612        0.638
##  1311   1916       1    0.624 0.006494        0.612        0.637
##  1314   1896       1    0.624 0.006499        0.612        0.637
##  1316   1890       1    0.624 0.006504        0.611        0.637
##  1317   1889       1    0.623 0.006509        0.611        0.636
##  1318   1888       1    0.623 0.006514        0.610        0.636
##  1319   1880       1    0.623 0.006519        0.610        0.636
##  1320   1871       1    0.622 0.006524        0.610        0.635
##  1321   1864       1    0.622 0.006529        0.609        0.635
##  1329   1818       2    0.621 0.006540        0.609        0.634
##  1332   1808       1    0.621 0.006545        0.608        0.634
##  1334   1792       1    0.621 0.006551        0.608        0.634
##  1336   1779       1    0.620 0.006556        0.608        0.633
##  1340   1766       1    0.620 0.006562        0.607        0.633
##  1342   1743       1    0.620 0.006568        0.607        0.633
##  1343   1737       1    0.619 0.006574        0.607        0.632
##  1350   1697       1    0.619 0.006580        0.606        0.632
##  1351   1692       2    0.618 0.006593        0.605        0.631
##  1355   1683       1    0.618 0.006599        0.605        0.631
##  1361   1641       2    0.617 0.006612        0.604        0.630
##  1362   1634       1    0.617 0.006619        0.604        0.630
##  1364   1622       1    0.616 0.006626        0.604        0.629
##  1367   1614       1    0.616 0.006633        0.603        0.629
##  1375   1561       1    0.616 0.006640        0.603        0.629
##  1377   1551       1    0.615 0.006648        0.602        0.628
##  1378   1542       1    0.615 0.006655        0.602        0.628
##  1379   1533       1    0.614 0.006663        0.601        0.628
##  1382   1525       1    0.614 0.006671        0.601        0.627
##  1387   1496       1    0.614 0.006679        0.601        0.627
##  1388   1495       1    0.613 0.006687        0.600        0.626
##  1393   1451       1    0.613 0.006696        0.600        0.626
##  1394   1450       1    0.612 0.006705        0.599        0.626
##  1396   1441       1    0.612 0.006713        0.599        0.625
##  1397   1434       2    0.611 0.006731        0.598        0.624
##  1408   1364       1    0.611 0.006741        0.598        0.624
##  1411   1354       2    0.610 0.006761        0.597        0.623
##  1419   1313       1    0.609 0.006772        0.596        0.623
##  1421   1301       1    0.609 0.006783        0.596        0.622
##  1428   1264       1    0.608 0.006795        0.595        0.622
##  1429   1262       2    0.607 0.006818        0.594        0.621
##  1438   1219       1    0.607 0.006831        0.594        0.620
##  1448   1181       2    0.606 0.006858        0.592        0.619
##  1450   1166       2    0.605 0.006885        0.591        0.618
##  1462   1124       1    0.604 0.006900        0.591        0.618
##  1463   1121       1    0.604 0.006915        0.590        0.617
##  1464   1120       1    0.603 0.006930        0.590        0.617
##  1466   1118       1    0.603 0.006944        0.589        0.616
##  1470   1111       1    0.602 0.006959        0.589        0.616
##  1472   1110       1    0.602 0.006974        0.588        0.615
##  1495    976       1    0.601 0.006994        0.587        0.615
##  1496    966       1    0.600 0.007015        0.587        0.614
##  1497    951       1    0.600 0.007035        0.586        0.614
##  1500    939       1    0.599 0.007057        0.585        0.613
##  1505    895       1    0.598 0.007081        0.585        0.612
##  1507    893       1    0.598 0.007104        0.584        0.612
##  1515    851       1    0.597 0.007131        0.583        0.611
##  1517    832       1    0.596 0.007158        0.582        0.610
##  1519    813       1    0.596 0.007187        0.582        0.610
##  1524    788       1    0.595 0.007217        0.581        0.609
##  1540    706       1    0.594 0.007256        0.580        0.608
##  1541    705       1    0.593 0.007295        0.579        0.608
##  1564    591       1    0.592 0.007351        0.578        0.607
##  1569    563       1    0.591 0.007413        0.577        0.606
##  1571    555       1    0.590 0.007475        0.575        0.605
##  1573    540       1    0.589 0.007541        0.574        0.604
##  1585    499       1    0.588 0.007618        0.573        0.603
##  1629    294       1    0.586 0.007850        0.570        0.601
##  1643    261       1    0.583 0.008134        0.568        0.600
##  1652    236       1    0.581 0.008467        0.565        0.598
##  1663    203       1    0.578 0.008896        0.561        0.596
##  1671    181       1    0.575 0.009402        0.557        0.594
##  1673    171       1    0.572 0.009930        0.552        0.591
##  1678    153       1    0.568 0.010545        0.548        0.589
##  1695    109       1    0.563 0.011664        0.540        0.586
```

---

### Kaplan-Meier estimates in R

```r
names(summary(dig_fit))
```

```
##  [1] "n"             "time"          "n.risk"        "n.event"      
##  [5] "n.censor"      "surv"          "std.err"       "cumhaz"       
##  [9] "std.chaz"      "type"          "logse"         "conf.int"     
## [13] "conf.type"     "lower"         "upper"         "call"         
## [17] "table"         "rmean.endtime"
```

---

### Kaplan-Meier estimates in R

```r
summary(dig_fit, time = 365)
```

```
## Call: survfit(formula = Surv(DWHFDAYS, DWHF) ~ 1, data = dig)
## 
##  time n.risk n.event survival std.err lower 95% CI upper 95% CI
##   365   5169    1188     0.82 0.00474        0.811        0.829
```

---

### Kaplan-Meier estimates in R

```r
plot(dig_fit)
```

---

### Kaplan-Meier estimates in R

```r
plot(dig_fit, main = "Kaplan-Meier estimate, all patients", 
     xlab = "Years",
     ylab = "Estimated survival probability",
     xscale = 365.25, conf.int = F)
```

---

### Kaplan-Meier estimates in R

```r
library(survminer)
ggsurvplot(survfit(Surv(DWHFDAYS, DWHF) ~ TRTMT, data = dig), 
           main = "Kaplan-Meier estimate by treatment group",
           xlab = "Days", 
           ylab = "Estimated survival probability",
           ylim = c(0, 1), conf.int = T, censor = F, 
           legend.labs = c("Placebo", "Digoxin"))
```

---

### Kaplan-Meier estimates in R