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R 尝试使用群集SEs进行mlogit时出错_R_Mlogit - Fatal编程技术网

R 尝试使用群集SEs进行mlogit时出错

R 尝试使用群集SEs进行mlogit时出错,r,mlogit,R,Mlogit,当我尝试将mlogit模型与集群SEs相匹配时,我不断收到以下错误: terms.formula中的错误(tmp,simplify=TRUE):“.”在公式中,没有“data”参数 这看起来类似于在SO上发现的其他问题,包括和,但这些并没有帮助我解决问题。我在df中没有NAs,我正在使用df中的所有列来适应模型,我在SEs上获得了无集群的mlogit()输出,并且我在cluster.bs.mlogit()函数中指定了dat=df2。我还删除了space2和time的固定效果,但仍然得到了错误。(

当我尝试将mlogit模型与集群SEs相匹配时,我不断收到以下错误:

terms.formula中的错误(tmp,simplify=TRUE):“.”在公式中,没有“data”参数

这看起来类似于在SO上发现的其他问题,包括和,但这些并没有帮助我解决问题。我在df中没有NAs,我正在使用df中的所有列来适应模型,我在SEs上获得了无集群的
mlogit()
输出,并且我在
cluster.bs.mlogit()
函数中指定了
dat=df2
。我还删除了space2和time的固定效果,但仍然得到了错误。(我知道在一个空间层次上聚类,在另一个空间层次上计算FEs有点奇怪)。以下是我一直在使用的代码:

df2 <- dfidx::dfidx(df, idx=list(c("id", "space1")), 
                          choice="outcome",shape="wide")
m1 <- mlogit(outcome ~  1 | cs1 + cs2  + cs3 + cs4 + cs5 + log(gpc) + log(p) + d + a + 
                        civ + nva + cp + ex + ex_sz + cs1:a + cs1:d + tnt + tvt + 
                        as.factor(space2) + as.factor(time), data=df2, reflevel = "p")
cluster_m1 <- clusterSEs::cluster.im.mlogit(m1,df2, ~space1)
df2
df <- structure(list(cs4 = c(2, 2, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 
1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 0, 
1, 2, 0, 2, 2, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 0, 1, 
0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0, 0, 1, 0, 1, 
0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 
0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 
1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 
0, 1, 0, 1, 2, 1, 2, 1, 0), cp = c(0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 
0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0), cs5 = c(0, 0, 3, 3, 0, 
0, 0, 3, 0, 1, 2, 4, 0, 0, 3, 3, 1, 0, 2, 0, 3, 3, 3, 0, 2, 1, 
0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 3, 0, 0, 0, 4, 1, 1, 
0, 3, 1, 0, 0, 0, 3, 0, 4, 1, 0, 0, 0, 0, 2, 1, 1, 2, 0, 0, 0, 
0, 0, 3, 3, 3, 2, 2, 3, 2, 3, 1, 2, 1, 1, 2, 1, 1, 3, 1, 1, 2, 
2, 3, 4, 3, 2, 1, 3, 2, 2, 3, 3, 4, 2, 1, 1, 2, 4, 0, 0, 1, 0, 
3, 2, 2, 0, 4, 3, 3, 3, 1, 2, 0, 2, 3, 4, 2, 2, 0, 3, 3, 3, 1, 
3, 2, 3, 4, 1, 3, 2, 2, 4, 2, 4, 3, 3, 4, 3, 1, 0, 1, 2, 2, 3, 
1, 3, 2, 2, 3, 3, 2, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0), nva = c(0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 
0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
), cs2 = c(1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 3, 2, 0, 0, 1, 2, 0, 
0, 1, 0, 1, 3, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 1, 0, 
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 
0, 0, 1, 0, 1, 2, 0, 1, 1, 0, 1, 3, 1, 2, 0, 2, 1, 3, 2, 3, 2, 
0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 1, 2, 0, 2, 3, 1, 3, 1, 2, 2, 3, 
2, 0, 0, 0, 0, 3, 4, 0, 2, 1, 2, 2, 4, 3, 1, 1, 0, 1, 0, 0, 1, 
2, 2, 2, 1, 1, 1, 4, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 
0, 1, 0, 2, 0), cs1 = c(1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 
1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 
0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 1, 0, 1, 0, 0), cs3 = c(0.375, 0.4, 0.2, 0.25, 0, 
0.273, 0.6, 0.25, 0.2, 0.25, 0.333, 0, 0.4, 0.333, 0.4, 0.143, 
0.333, 0.1, 1, 0.5, 0.333, 0.5, 0, 0, 1, 0, 0.333, 0.6, 1, 0.667, 
0.2, 0.667, 0.4, 0, 0.667, 0.667, 0, 0.571, 1, 0.5, 0.333, 0, 
0, 0.667, 0, 0.375, 0.125, 0.455, 0.167, 0, 0.6, 0.4, 0.333, 
0, 0.6, 0.2, 0.333, 0, 0.2, 0.1, 0.364, 0, 0.222, 0.4, 0.2, 0.4, 
1, 0.6, 0.8, 0, 0.2, 0.5, 0, 0.4, 0.25, 0.375, 0.8, 0, 0.571, 
0.4, 0.6, 0.6, 0.143, 0.333, 0.2, 0.2, 0.5, 0.4, 0.2, 0.4, 0.4, 
0, 0.167, 0.429, 0.25, 0, 0.4, 0, 0.2, 0, 0, 0.167, 0.167, 0.429, 
0.2, 0, 0.312, 0.4, 0.273, 0.364, 0.4, 0.143, 0.6, 0.429, 0.5, 
0.2, 0.167, 0, 0.5, 0.5, 0.833, 0.143, 0.333, 0.2, 0, 0, 0.75, 
0.167, 0, 0.4, 0.375, 0.2, 0.667, 0, 0, 1, 0, 0.167, 0.2, 0, 
0.1, 0, 0, 0.143, 0, 0.429, 0.167, 0, 0, 0.143, 0.333, 0.333, 
0, 0, 0.167, 0.333, 0.143, 0.4, 0.4, 0.333, 0, 0.286, 0.833, 
0, 0.6, 0, 0.167, 0, 1), gpc = c(20008.83, 22945.88, 3434.72, 
1367.25, 4635.25, 4025.94, 25326.29, 8432.21, 2006.06, 2638, 
386.46, 4265.92, 4277.63, 8508.3, 3253.99, 10138.66, 2883.43, 
5164.21, 4220.69, 3545.15, 2233.13, 2347.77, 1628.45, 9743.05, 
2173.55, 7297.21, 30865.49, 5323.74, 20071, 24466.92, 56457.18, 
16729, 26505.99, 5025.13, 8654.35, 13189.99, 15150.58, 14957.6, 
18159.85, 11204.66, 5997.27, 15904.75, 13625.07, 5207.7, 4567.62, 
11135.74, 5322.99, 15013.91, 4475.24, 1295.67, 19399.23, 11799.84, 
20804.08, 3714.26, 4119.68, 3324.48, 20057.46, 16130.93, 7425.79, 
14122.05, 6049.24, 8568.5, 5494.57, 3150.87, 2503.37, 9202.88, 
10225.27, 29733.63, 18185.93, 1364.95, 748.27, 931.02, 1011.1, 
414.03, 1711.81, 1450.74, 1790.61, 1169.21, 2014.03, 1697.39, 
538.56, 1112.74, 1071.77, 1818, 807.46, 1311.09, 591.03, 8066.15, 
660.71, 1045.19, 3291.11, 900.77, 915.94, 1269.9, 917.89, 620.37, 
866.45, 1304.6, 3415.19, 434.46, 522.25, 2606.63, 340.27, 945.27, 
2895.07, 692.12, 7530.58, 4291.67, 1287.58, 9936.33, 2590.57, 
1026.56, 1607.14, 10562.02, 1761.87, 2461.54, 2021.17, 4570.87, 
1295.29, 2935.65, 4212.87, 4261.05, 4082.48, 1373.31, 3400.13, 
4279.53, 18284.59, 18478.7, 1316.04, 2161.06, 35015.64, 16253.03, 
40038.46, 26731.36, 1149.98, 911.96, 5501.82, 2997, 2165.62, 
3466.05, 11047.72, 849.08, 1098.75, 5385.09, 2104.84, 1807.55, 
1764.25, 1458.03, 574.95, 1839.78, 1166.65, 971.96, 2263.42, 
985.58, 7593.18, 1811.9, 1901.39, 869.74, 1188.73, 2950.01, 23854.89, 
3273.33, 3493.45, 1700.53, 25580.73, 1815.35, 13162.1, 2329.24, 
3901.38), civ = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 
0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0), p = c(205024.36, 23975.64, 11157, 6625, 
7631.08, 2709.04, 1117.46, 58492.12, 3276.11, 5963.01, 2117.92, 
2352, 1210.85, 3181.97, 14888.58, 4973, 633, 519.86, 6519.79, 
17286.83, 80999.11, 4877.27, 2014.46, 14409.42, 17165.4, 3029.95, 
62035.57, 2949.63, 13814.86, 10079.87, 507.45, 53168.33, 6340.82, 
30564.56, 9070.91, 60842, 16640, 38189.76, 7570.91, 10376.32, 
15314, 10319.92, 5411.34, 49165.9, 2777.59, 627.07, 2001.18, 
4433.79, 20029, 3462.03, 1988.39, 9848.05, 758, 7798, 4375.24, 
20863.94, 148673.81, 1344.04, 2528.89, 3341.1, 46923.93, 9872.11, 
3074.18, 4626.03, 7764.8, 4460.7, 7314.58, 3786.02, 5038.75, 
348.17, 1240.66, 362.32, 1158.31, 5303.49, 3551.78, 3917.94, 
1201.46, 4372.96, 6180, 6871.53, 5675.28, 1706.54, 3093.34, 8637.72, 
4926.14, 6364, 102444.77, 1177.94, 3632.29, 6998.11, 2325.04, 
22658.91, 9161.91, 11252.32, 10704.74, 3910.12, 3528.64, 6289, 
340.13, 22849.9, 4134, 15957.46, 13867.42, 9418.12, 9523.38, 
9721.62, 50132.82, 2242.08, 2127.41, 1981.58, 639.38, 7297.71, 
340.78, 1196.03, 15310, 11460, 4921.41, 3821, 10544, 54870.58, 
29543.62, 5610, 67648.42, 11966.27, 1535, 3260.5, 4291.63, 16139.05, 
3797, 1515, 432, 532.36, 459.95, 1398, 474, 13984, 4335.99, 6691.42, 
5008.35, 24469.44, 15476.09, 697704.58, 1523.91, 15505.12, 22097, 
30763.28, 83295.25, 964486.16, 702, 92300.28, 92283.6, 36943, 
10939.73, 18624.19, 67796.45, 16408.08, 5667.05, 19850, 16540, 
8662.72, 2646.96, 63146.88, 197330.13, 1141.41, 16596.1, 5821, 
2584.2, 437, 565.43), d = c(1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 
0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 
1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 
0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 
0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 
0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1), a = c(0, 0, 0, 0, 0, 0, 0, 
0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 
0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 
1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 
1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0), space2 = c(1, 1, 
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 
2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 
4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5), 
    time = c(3, 4, 7, 6, 6, 7, 5, 4, 2, 6, 2, 4, 2, 7, 2, 2, 
    3, 8, 4, 5, 3, 4, 3, 6, 2, 5, 8, 2, 4, 6, 8, 4, 4, 3, 4, 
    4, 5, 7, 5, 6, 5, 6, 7, 2, 5, 7, 7, 7, 3, 6, 7, 5, 7, 3, 
    6, 4, 6, 7, 6, 8, 7, 7, 7, 7, 6, 3, 2, 3, 4, 6, 7, 6, 6, 
    3, 3, 5, 4, 4, 4, 6, 3, 4, 5, 3, 7, 4, 6, 6, 7, 6, 6, 4, 
    4, 4, 3, 4, 3, 5, 5, 2, 7, 7, 6, 6, 5, 6, 8, 8, 7, 8, 5, 
    4, 5, 7, 4, 3, 3, 5, 2, 6, 3, 2, 7, 6, 2, 6, 5, 6, 2, 4, 
    3, 6, 6, 5, 2, 4, 6, 7, 7, 7, 7, 3, 4, 4, 6, 4, 2, 6, 2, 
    5, 5, 5, 3, 6, 7, 7, 7, 3, 3, 3, 5, 6, 6, 8, 5, 7, 3, 7, 
    4), tnt = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 
    0, 0), tvt = c(0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
    0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 
    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 
    0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 
    0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 
    0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 
    0, 0, 0), ex = c(1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 
    1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 
    1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 
    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 
    1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 
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