CopyrightSupplement: Model Code for WinBUGS.
The code included here implements Model 1, a simple GLM, and Model 2, a simple, single-level spatial model. Models 3 and 4 cannot currently be implemented in WinBUGS and require custom coding. For the purpose of these examples, we include data for a small region including 476 one minute by one minute grid cells. This region is is a small corner of South Africa's Cape Floristic Region, and includes very high plant species diversity and a World Biosphere Reserve. The sample data set includes (see Table S1):
1) n[i] = the number of visits or sample locations in each cell (which can be zero);2) y[i] =the number of times the species was observed to be present in each cell;3) a set of environmental covariates: Elevational range or "roughness" (rough[i]), July minimum temperature (julmint[i]), interannual variation in precipitation (pptcv[i]), summer soil moisture days (smdsum[i]), enhanced vegetation or "greenness" index (evi[i]), and percent acidic soil (ph1[i]); and4) adj[i] = the spatial position of each grid cell, expressed as a list of adjacent cells. Together with num[i] = number of neighbors of each cell, this is a sparse representation of the adjacency matrix for the subregion.
Cell Samples (ni) Presences (yi) Covariates (x1i, ... , x6i) Adjacent cells 1 7 0 -0.901, ..., -1.109 2, 18, 19 2 7 0 -0.603, ..., -1.957 1, 3, 18, 19, 20 ... ... ... ... ... 476 2 0 -1.372, ..., -1.723 458, 459, 475 The non-spatial model, Model 1, can be written as:
For ni >0,
yi ~ Binomial(ni, pi)
logit(pi) = mu + x1i * beta1 + x2i * beta2 + x3i * beta3 + x4i * beta4 + x5i * beta5 + x6i * beta6
Note that for ni =0, there is no contribution of grid cell i to the likelihood. Accordingly, the code includes an index vector, ind[], to hold the row numbers of the sampled cells, and an integer variable, N_nonzeroy, that stores the number of sampled cells.
The spatial model, Model 2, adds a set of spatial random effects (Rho[i]):
For ni >0,
yi ~ Binomial(ni, pi)
logit(pi) = mu + rhoi + x1i * beta1 + x2i * beta2+ x3i * beta3 + x4i * beta4 + x5i * beta5 + x6i * beta6
We assume a CAR prior for rho. Note that for unvisited sites, the inference for rhoi is entirely by "borrow strength" from its neighbors.
model
{# likelihood
for (i in 1 : N_nonzeroy) {
y[ind[i]] ~ dbin(p[ind[i]], n[ind[i]])
}
for(i in 1:N_LOC){
logit(p[i]) <- xbeta[i]+mu
xbeta[i]<-beta[1]*rough[i] + beta[2]*julmint[i] + beta[3]*pptcv[i] + beta[4]*smdsum[i] + beta[5]*evi[i] + beta[6]*ph1[i]
}
temp<-adj[1]+sumNumNeigh+num[1] # junk node to hold unused variables# priors
mu ~ dnorm(0,0.1)
for ( i in 1:6) { beta[i] ~ dnorm(0, 0.2) }
}
model
{# likelihood
for (i in 1 : N_nonzeroy) {
y[ind[i]] ~ dbin(p[ind[i]], n[ind[i]])
}
for(i in 1:N_LOC){
logit(p[i]) <- rho[i]+xbeta[i]+mu
xbeta[i]<-beta[1]*rough[i] + beta[2]*julmint[i] + beta[3]*pptcv[i] + beta[4]*smdsum[i] + beta[5]*evi[i] + beta[6]*ph1[i]
}# CAR prior distribution for spatial random effects:
rho[1:N_LOC] ~ car.normal(adj[], weights[], num[], tau)
for(k in 1:sumNumNeigh) {
weights[k] <- 1 # set equal weights for all neighbors
}# other priors
mu ~ dnorm(0,0.1)
for ( i in 1:6) { beta[i] ~ dnorm(0, 0.2) }
vrho ~ dnorm(0, 0.2) I(0,)
tau <- 1/vrho
}
list( N_LOC=476, N_nonzeroy=351,
y=c(0, 0, 0, 0, 0, 3, 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, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 16, 25, 0, 0, 0, 0, 9, 1, 0, 0, 0, 0, 0, 0, 1, 3, 17, 18, 0, 2, 4, 5, 2, 3, 0, 0, 10, 15, 0, 0, 0, 0, 1, 6, 0, 3, 18, 13, 5, 0, 2, 0, 0, 19, 13, 0, 0, 0, 0, 2, 7, 20, 7, 23, 5, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 5, 4, 6, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 6, 1, 1, 1, 6, 5, 1, 0, 0, 0, 0, 0, 0, 0, 2, 9, 9, 7, 0, 0, 0, 0, 7, 4, 4, 0, 0, 0, 0, 0, 3, 14, 1, 1, 0, 0, 0, 0, 0, 0, 7, 3, 0, 0, 0, 2, 4, 8, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 1, 2, 0, 2, 4, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 9, 4, 1, 0, 0, 7, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 6, 7, 9, 11, 8, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 5, 16, 15, 20, 7, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 24, 10, 8, 7, 4, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 4, 8, 3, 4, 3, 1, 1, 3, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 8, 5, 2, 4, 5, 2, 1, 2, 0, 0, 0, 0, 0, 1, 7, 3, 9, 5, 6, 10, 6, 9, 16, 1, 1, 10, 13, 1, 1, 0, 5, 10, 7, 19, 8, 2, 20, 23, 5, 6, 6, 28, 23, 1, 2, 0, 0, 6, 6, 15, 6, 12, 9, 4, 6, 10, 15, 103, 31, 5, 0, 1, 0, 1, 0, 2, 1, 5, 3, 9, 37, 33, 15, 15, 55, 11, 2, 1, 1, 0, 0, 0, 8, 5, 5, 15, 19, 69, 14, 15, 16, 3, 0, 0, 0, 0, 0, 0, 0),
n=c(0, 0, 1, 4, 3, 7, 1, 3, 1, 0, 1, 3, 6, 13, 5, 2, 0, 0, 0, 0, 0, 2, 0, 1, 4, 9, 0, 1, 0, 4, 9, 9, 8, 0, 0, 1, 4, 3, 0, 0, 0, 2, 8, 4, 0, 2, 6, 8, 5, 0, 0, 0, 0, 29, 3, 2, 2, 0, 1, 0, 4, 0, 3, 1, 1, 3, 3, 0, 0, 0, 6, 1, 10, 19, 3, 8, 8, 0, 1, 0, 0, 2, 4, 1, 0, 1, 0, 1, 4, 8, 22, 18, 10, 25, 15, 1, 3, 4, 1, 0, 0, 0, 0, 1, 2, 3, 1, 13, 16, 12, 40, 41, 31, 0, 1, 0, 1, 31, 6, 0, 0, 0, 4, 2, 3, 7, 6, 18, 18, 2, 5, 4, 6, 7, 5, 3, 1, 49, 37, 1, 0, 1, 5, 7, 12, 0, 3, 22, 16, 6, 0, 2, 0, 4, 135, 35, 0, 1, 4, 5, 6, 10, 21, 7, 32, 7, 5, 1, 1, 0, 0, 3, 4, 0, 3, 0, 3, 0, 1, 0, 10, 8, 15, 10, 1, 0, 0, 0, 1, 2, 1, 0, 0, 4, 1, 0, 0, 0, 8, 12, 18, 1, 0, 0, 1, 1, 12, 5, 7, 7, 10, 10, 2, 6, 1, 2, 1, 8, 6, 1, 1, 4, 0, 1, 0, 0, 6, 10, 9, 11, 8, 0, 1, 1, 0, 8, 4, 5, 0, 3, 0, 2, 11, 26, 17, 1, 1, 1, 0, 0, 0, 1, 0, 9, 3, 0, 1, 4, 6, 12, 14, 6, 7, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 12, 14, 4, 0, 3, 9, 9, 3, 0, 31, 0, 0, 0, 0, 0, 0, 14, 6, 2, 0, 0, 8, 5, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 17, 10, 11, 10, 11, 8, 3, 7, 1, 0, 0, 0, 0, 0, 1, 2, 0, 24, 6, 16, 20, 21, 9, 6, 10, 0, 0, 0, 3, 2, 0, 0, 7, 0, 8, 14, 33, 15, 8, 8, 18, 10, 12, 5, 29, 38, 3, 0, 3, 3, 2, 1, 12, 5, 9, 5, 4, 4, 7, 13, 11, 3, 5, 6, 2, 0, 9, 6, 5, 7, 5, 9, 7, 6, 5, 10, 4, 5, 19, 25, 0, 1, 2, 2, 6, 7, 3, 12, 11, 12, 13, 9, 14, 24, 27, 20, 31, 17, 2, 1, 2, 12, 15, 8, 20, 10, 4, 30, 26, 7, 7, 7, 32, 24, 1, 3, 0, 0, 9, 28, 26, 7, 17, 12, 8, 38, 55, 30, 145, 35, 9, 0, 3, 0, 4, 3, 5, 6, 9, 4, 10, 51, 53, 18, 26, 126, 30, 34, 4, 2, 4, 4, 0, 25, 7, 11, 29, 22, 89, 18, 22, 26, 4, 0, 0, 0, 0, 2, 0, 2),
ind=c(3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 22, 24, 25, 26, 28, 30, 31, 32, 33, 36, 37, 38, 42, 43, 44, 46, 47, 48, 49, 54, 55, 56, 57, 59, 61, 63, 64, 65, 66, 67, 71, 72, 73, 74, 75, 76, 77, 79, 82, 83, 84, 86, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 117, 118, 119, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 147, 148, 149, 150, 152, 154, 155, 156, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 172, 173, 175, 177, 179, 181, 182, 183, 184, 185, 189, 190, 191, 194, 195, 199, 200, 201, 202, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 224, 227, 228, 229, 230, 231, 233, 234, 236, 237, 238, 240, 242, 243, 244, 245, 246, 247, 248, 252, 254, 255, 257, 258, 259, 260, 261, 262, 263, 264, 272, 274, 275, 276, 278, 279, 280, 281, 283, 290, 291, 292, 295, 296, 297, 304, 307, 308, 309, 310, 311, 312, 313, 314, 315, 321, 322, 324, 325, 326, 327, 328, 329, 330, 331, 335, 336, 339, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 439, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 474, 476),
rough=c(-0.901, -0.603, -0.553, -0.667, 0.536, 1.186, 0.261, -0.91, 0.005, 0.701, -0.132, 0.321, -0.237, 0.326, -0.361, -0.818, -0.832, -1.098, -0.663, -0.764, -0.631, -0.832, -0.919, -1.084, 1.044, 2.463, 2.691, 0.907, 1.378, 0.797, 0.248, -0.498, -0.338, -1.189, -0.837, -1.29, -1.07, -0.576, 0.907, 1.126, -0.361, 2.408, 1.099, 0.92, 1.314, 1.872, 0.916, -0.32, -0.073, 0.197, -1.143, -1.198, -0.8, 0.888, 0.719, 0.55, 1.236, 1.392, 1.305, 2.261, 0.833, 2.618, 2.014, 1.671, 0.751, 1.007, 0.563, 0.952, -1.139, -0.8, 1.383, 2.604, 1.465, -0.558, 1.891, 2.389, 1.968, 1.689, 1.099, 0.646, 1.611, 0.449, 0.257, 1.529, 1.794, -1.066, -0.933, 0.65, 1.758, 2.074, 2.032, 0.431, 1.465, 3.108, 1.424, 1.534, 1.36, 1.314, 2.508, 1.639, 1.058, 1.648, -1.084, -0.8, -0.718, 1.703, 1.168, 1.149, 1.442, 1.817, 1.264, 1.753, 0.939, 1.694, 1.113, 0.563, 1.323, 0.184, -0.265, -0.494, 0.065, 1.017, 0.184, 1.085, -0.109, 1.941, 1.236, 0.925, 0.152, 0.696, 0.106, 0.531, 0.275, 0.435, 0.426, -1.239, -0.224, 1.017, 1.863, 0.673, -0.031, -0.69, -0.393, 2.339, 0.577, 0.454, 0.358, 1.575, 1.552, -0.123, 0.445, -0.361, -1.253, -0.192, 0.362, 0.293, -0.571, -1.121, -0.974, -0.219, 2.142, 0.605, 0.696, -0.182, -0.388, -0.063, 0.138, 0.44, -0.896, -1.258, -0.823, -0.878, -0.951, -1.221, -0.965, -0.626, 0.165, 2.133, 0.847, 0.504, 0.147, 0.472, -0.599, -0.041, -0.841, -1.116, -0.997, -1.185, -0.86, -0.649, -0.613, -0.855, -0.704, 0.17, 2.17, 1.09, 1.419, 1.035, 0.554, -0.475, 0.229, -0.741, -0.924, -0.846, -1.317, -0.873, -0.489, -0.695, -0.741, -0.892, -0.009, 1.346, 1.021, 1.122, -0.315, 0.014, -0.645, -0.182, 0.49, 0.39, -0.603, -1.345, -1.221, -0.718, -0.695, -0.947, -0.933, 0.646, 0.078, 0.046, 0.403, -0.549, -0.562, -0.603, 0.426, 0.005, 0.82, 0.545, -1.363, -1.336, -1.272, -1.111, -0.645, 0.33, -0.091, -0.654, -0.846, -0.677, -0.965, -1.153, -1.075, -0.407, 0.984, 1.502, 0.239, -1.395, -1.326, -0.814, 0.518, 0.316, -0.32, -0.992, -1.262, -0.96, -1.235, -1.189, -1.262, -1.102, -1.052, -1.052, -0.018, 0.445, -0.484, 0.696, 0.82, -0.246, -0.818, -0.924, -1.034, -1.029, -1.061, -0.97, -1.194, -1.217, -1.226, -1.125, -1.18, -0.91, -0.228, -0.603, -1.102, -1.198, -0.663, -0.384, -0.224, -0.361, -0.663, -0.777, -1.139, -1.175, -1.217, -1.079, -1.066, -1.034, -1.102, -0.883, 0.367, -0.192, -0.009, -0.086, 0.184, -0.654, 0.293, -0.343, -1.239, -0.979, -0.928, -1.107, -0.979, -1.029, -1.121, -1.116, -0.837, -0.562, -0.173, 0.11, 0.554, 0.801, 0.838, 0.554, -1.029, -1.139, -0.873, -0.855, -0.759, -0.832, -1.088, -1.143, -0.466, -0.581, 0.312, 1.749, 2.879, 1.113, 0.806, -0.013, -0.64, -1.121, -1.212, -0.841, -0.979, -1.07, -1.111, -1.056, -1.047, -0.494, -0.494, -1.322, 0.115, 1.685, 0.783, 0.188, -0.036, -0.732, -1.111, -1.171, -0.974, -0.974, -1.075, -1.079, -1.088, -0.924, -0.695, -0.228, 1.323, 1.648, 1.049, 0.115, 0.902, 0.271, 0.248, -0.439, -0.173, -0.526, -0.805, -0.594, -0.507, -0.466, -0.471, -0.43, -0.777, 0.138, 0.765, 0.207, -0.315, -0.279, -0.036, 1.172, 1.131, -0.411, -0.562, 0.33, -0.05, -0.805, -0.818, -1.23, -0.75, -0.114, 0.184, -0.265, -0.526, 0.101, 0.353, 0.046, 0.55, 0.426, 0.367, 0.261, -0.503, -0.613, 0.289, -0.05, -0.704, -0.823, -0.329, 0.925, 1.049, 0.412, 0.005, 0.577, 1.405, 1.41, 0.458, 0.605, 0.669, 0.261, 0.71, 0.568, -0.416, 0.051, 0.028, -0.05, -0.448, -0.082, 0.669, 0.888, 1.081, 1.017, 1.451, 0.129, -0.489, 0.87, 0.847, -0.672, -0.809, -0.965, -1.07, -1.244, -1.281, -0.75, -0.027, 1.579, 2.179, 0.815, 0.893, 1.085, 0.87, -0.718, -1.313, -1.299, -1.326, -1.377, -1.372, -1.354, -1.345, -1.372),
julmint=c(0.393, 0.148, 0.148, 0.148, -0.343, -0.588, -0.098, 0.025, -0.098, -0.466, -0.098, -0.098, -0.098, -0.711, -0.343, -0.343, -0.466, 0.638, 0.393, 0.393, 0.025, -0.22, -0.098, 0.025, -0.22, -0.956, -2.428, -1.324, -1.201, -0.466, -0.343, -0.343, -0.833, -0.466, 0.638, 0.516, 0.516, 0.27, -0.22, -0.466, -0.098, -0.466, -2.796, -3.286, -2.183, -1.324, -0.343, -0.098, -0.343, -0.711, -0.466, 0.761, 0.638, 0.148, 0.393, 0.148, -0.588, -1.079, -0.343, -0.833, -2.183, -1.201, -1.079, -1.079, -1.079, -0.833, -0.833, -0.588, 0.761, 0.638, 0.025, -1.815, 0.025, 0.27, -0.22, -2.183, -2.796, -0.22, -3.532, -3.041, -1.201, -0.466, -0.343, -0.956, -3.286, 0.761, 0.761, 0.393, -0.833, -1.815, -0.466, 0.148, -0.22, -0.833, -2.918, -3.041, -0.711, -0.343, -0.833, -0.956, -2.55, -1.079, 0.883, 0.638, 0.638, -0.343, -1.079, -2.06, -0.466, -1.079, -0.956, -0.588, -2.673, -1.201, -2.305, -3.286, -1.079, -0.343, -0.343, 0.638, 0.516, 0.148, 0.27, -0.466, -0.098, -0.343, -1.815, -2.673, -2.183, -2.673, -3.164, -2.673, -1.447, -1.079, -0.343, -0.343, 0.638, -0.098, -0.466, 0.393, 0.516, 0.393, 0.27, -0.833, -3.409, -2.796, -2.06, -0.711, -1.201, -1.079, -1.079, -0.22, -0.22, 0.638, 0.516, 0.761, 0.761, 0.883, 0.638, 0.148, -0.588, -2.06, -2.55, -1.937, -1.079, -0.833, -0.22, -0.466, -0.22, -0.22, 1.129, 1.129, 1.129, 1.006, 0.883, 0.638, 0.025, -0.833, -2.55, -2.06, -2.06, -1.201, -0.588, -0.588, -0.098, -0.22, -0.22, 1.374, 1.251, 1.129, 1.006, 0.761, 0.638, 0.148, -0.466, -2.183, -0.588, -0.956, -0.833, -0.466, -0.466, -0.22, -0.22, -0.343, 1.374, 1.129, 0.883, 0.761, 0.638, 0.638, 0.27, -1.937, -0.711, -0.833, -0.22, -0.22, -0.22, -0.956, -0.833, -0.833, -0.466, 1.497, 1.374, 1.251, 1.129, 1.006, 0.761, 0.27, -0.711, -0.22, -0.22, 0.148, 0.148, 0.025, -0.343, -1.937, -1.201, -1.447, 1.497, 1.497, 1.374, 1.251, 1.006, 0.761, 0.025, 0.148, 0.025, 0.148, 0.148, 0.148, 0.148, -0.098, -0.343, -0.956, -2.305, 1.405, 1.497, 1.497, 1.251, 0.638, 0.393, 0.393, 0.148, 0.27, 0.27, 0.27, 0.27, 0.148, 0.025, -0.098, -0.343, -0.711, 1.08, 1.129, 0.27, 0.638, 0.638, 0.393, 0.27, 0.148, 0.27, 0.27, 0.393, 0.27, 0.148, 0.025, -0.098, 0.025, -0.098, 1.006, 1.006, 0.638, 0.516, 0.27, -0.098, 0.148, 0.27, 0.393, 0.516, 0.27, 0.148, 0.148, 0.025, 0.025, 0.148, 0.025, 0.025, 0.516, 0.148, -0.098, -0.343, -0.343, -0.22, 0.516, 0.516, 0.393, 0.393, 0.27, 0.393, 0.393, 0.27, 0.27, 0.025, 0.393, 0.148, 0.025, -1.815, -0.466, -0.098, 0.516, 0.638, 0.516, 0.516, 0.516, 0.516, 0.516, 0.393, 0.516, 0.393, -0.098, 1.497, 0.883, -0.588, -1.569, -0.466, 0.516, 0.638, 0.638, 0.638, 0.516, 0.761, 0.761, 0.516, 0.638, 0.516, 0.516, 0.393, 1.055, 1.251, 0.638, -0.466, -0.588, 0.27, 0.638, 0.638, 0.638, 0.516, 0.638, 0.761, 0.761, 0.761, 0.638, 0.516, 0.27, 1.619, 0.025, -0.22, 0.393, 0.761, -0.22, 0.148, 0.148, 0.516, 0.761, 0.761, 0.761, 0.638, 0.761, 0.516, 0.27, 0.148, 0.516, 0.393, 0.638, 0.883, 0.761, 0.883, 0.761, 0.516, 1.006, 1.006, 0.761, 0.516, 0.27, 0.148, 0.27, 0.393, 0.393, 1.006, 0.761, 0.393, 0.761, 0.516, 0.638, 0.638, 0.393, 0.393, 0.516, 0.025, 0.148, 0.516, 0.883, 0.393, 0.393, 0.761, 1.129, 0.516, 0.025, 0.148, -0.098, -0.098, 0.761, 1.251, 1.006, 0.393, 0.516, 1.006, 0.393, 1.251, 0.638, 0.883, 1.129, 1.374, 0.761, 0.148, 0.148, 1.006, 0.516, 0.883, 0.761, 1.129, 1.006, 1.129, 1.374, 1.374, 1.374, 1.374, 1.251, 1.374, 1.251, 1.374, 1.006, 0.883, 1.374, 1.251, 0.761, 0.638, 0.883, 1.088, 1.17, 1.292, 1.374, 1.405, 1.497, 1.374, 1.272),
pptcv=c(1.648, 1.477, 0.792, 0.472, 0.151, -0.298, -1.025, -0.148, -0.426, -1.025, -1.025, -1.025, -0.533, -0.127, 0.771, 0.707, 0.878, 1.498, 1.69, 1.135, 0.408, 0.065, -0.341, -0.982, -0.683, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, 0.001, 0.215, 0.857, 1.755, 1.37, 1.263, 0.771, 0.386, -0.148, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, 0.728, 1.733, 1.241, 0.686, 0.878, 0.514, -0.982, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, 0.044, 1.776, 0.921, 0.301, -1.025, -0.683, -0.491, -0.426, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.982, -1.025, -1.025, 1.648, 0.942, 0.343, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, 1.519, 1.006, 0.408, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.875, 1.584, 1.263, 0.408, -0.041, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.726, -0.255, 1.733, 0.814, -0.191, -0.213, 0.194, -0.277, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.747, 0.6, 1.776, 2.011, 1.584, 0.365, 0.878, 0.108, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.255, 0.963, 2.118, 2.503, 2.396, 0.108, 0.921, 0.386, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.362, 0.194, 1.049, 1.712, 2.482, 2.503, 1.776, 1.284, 0.429, -1.004, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.469, -0.405, 0.023, 2.075, 2.439, 2.353, 1.926, 1.177, 0.151, -0.875, -1.025, -1.025, -1.025, -1.025, -1.025, -0.79, -1.025, -0.918, -1.025, -0.576, 2.033, 2.097, 1.947, 1.669, 1.284, 0.301, -0.918, -1.025, -1.025, -1.025, -1.025, -0.769, 0.13, -0.213, -1.025, -1.025, -1.025, 1.584, 1.562, 1.498, 1.519, 1.306, 0.621, -0.64, -0.555, -1.025, -1.025, -0.469, 0.087, 0.45, 0.301, -0.234, -1.025, -1.025, 1.38, 1.413, 1.434, 1.37, 0.514, 0.472, 0.001, -0.533, -0.277, -0.747, -0.491, -0.041, 0.643, 0.386, 0.322, -0.063, -0.811, 0.643, 1.263, -0.191, 0.065, -0.341, -0.106, -0.491, -0.234, -0.17, 0.365, -0.426, 0.621, 1.391, 1.284, 0.921, 0.664, 0.514, 0.429, 0.215, 0.001, -0.448, -0.704, -1.004, -0.426, -0.683, -0.041, 0.13, 0.664, 1.434, 1.455, 1.797, 1.413, 1.648, 1.135, -0.341, -0.533, -1.025, -1.025, -1.025, -1.025, -1.025, -0.854, -0.127, 0.814, 0.878, 1.199, 1.327, 1.37, 1.669, 1.69, 1.455, -0.298, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.277, 0.536, 0.707, 1.199, 1.391, 1.584, 1.562, 1.562, 1.306, 0.899, -0.277, -1.025, -1.025, -1.025, -1.025, -1.025, -1.025, -0.576, 0.835, 0.878, 1.37, 1.584, 1.498, 1.434, 1.37, 1.306, 0.151, 1.113, -0.769, -1.025, -1.025, -1.025, -0.961, -0.854, 0.023, 0.985, 0.857, 1.092, 1.156, 1.199, 1.177, 1.263, 1.177, 0.087, -1.025, -1.025, -1.025, -1.025, -1.025, -0.769, 0.044, 0.386, -0.106, 0.857, 0.963, 1.07, 1.049, 1.049, 0.921, 0.942, 0.044, -0.041, -1.025, -1.025, 0.044, -0.127, -0.127, -0.277, -0.17, 0.878, 0.835, 0.728, 0.579, 0.814, 0.835, 0.386, 0.493, 0.835, 0.557, -0.405, -0.662, 0.172, -0.597, -0.448, -0.191, 0.365, 0.536, 0.172, 0.258, 0.408, 0.236, 0.6, 0.536, 0.75, 1.327, 0.408, -0.106, -0.533, -0.811, -1.025, -0.405, -0.426, 0.75, 0.301, 0.065, 0.408, 0.236, 0.536, 0.857, 1.028, 1.177, 1.541, -1.025, -0.405, -1.025, -1.025, -1.004, -0.875, -0.127, 0.151, 1.049, 0.643, 0.835, 0.707, 0.899, 1.413, 1.07, 0.857, 1.37, 1.434, 0.771, -0.726, -0.811, -0.448, -0.191, 0.215, 0.204, 0.472, 0.686, 0.614, 0.757, 1.113, 1.605, 1.296, 1.461),
smdsum=c(-1.372, -1.26, -0.979, -0.851, -0.699, -0.512, -0.179, -0.52, -0.52, -0.247, -0.247, -0.36, -0.676, -0.906, -1.328, -1.439, -1.282, -1.335, -1.476, -1.162, -0.812, -0.643, -0.448, -0.161, 0.667, 0.667, 1.594, 1.065, 0.761, -0.248, -0.36, -1.025, -1.137, -1.315, -1.43, -1.253, -1.188, -0.942, -0.751, -0.486, -0.023, 2.424, 2.424, 2.002, 1.962, 1.324, 0.509, 0.755, 0.468, -0.558, -1.182, -1.405, -1.176, -0.912, -0.963, -0.773, -0.028, 0.809, 1.376, 1.376, 2.033, 1.49, 1.354, 1.094, 0.721, 0.195, -0.425, -0.867, -1.409, -1.016, -0.722, 0.662, -0.163, -0.171, -0.197, 3.283, 3.283, 0.455, 1.992, 2.892, 1.509, 0.655, -0.43, -0.059, 1.018, -1.345, -1.016, -0.727, 0.368, 0.654, 0.412, 0.653, 1.716, 1.716, 1.637, 3.056, 1.448, 0.772, 0.741, 0.464, 1.138, -0.082, -1.289, -1.048, -0.757, 0.143, 0.667, 1.2, 0.702, 1.909, 1.909, 1.253, 2.868, 1.758, 1.805, 2.185, 0.744, -0.108, -0.458, -1.314, -1.176, -0.761, -0.514, 0.2, 0.426, 0.746, 2.773, 2.773, 2.46, 2.376, 2.63, 1.884, 1.089, 0.609, -0.497, -0.726, -1.396, -0.998, -0.535, -0.443, -0.586, -0.331, 0.292, 3.325, 3.325, 2.272, 2.08, 1.3, 1.302, 0.879, 0.525, -0.498, -1.089, -1.413, -1.568, -1.394, -0.689, -0.884, -0.499, 0.093, 2.104, 2.104, 2.002, 1.797, 1.427, 1.1, 0.303, -0.262, -0.723, -1.279, -1.409, -1.833, -1.918, -0.874, -0.978, -0.611, 0.197, 2.181, 2.181, 1.747, 1.796, 1.209, 0.602, 0.021, -0.573, -0.783, -1.231, -1.4, -1.719, -1.753, -1.385, -1.039, -0.607, 0.101, 1.813, 1.813, 1.323, 1.321, 0.934, 0.245, -0.03, -0.323, -0.358, -0.663, -1.435, -1.59, -1.542, -1.364, -0.962, -0.491, 0.079, 1.246, 1.246, 1.366, 0.842, 0.405, -0.163, -0.047, 0.095, 0.077, -0.165, -1.396, -1.43, -1.347, -1.204, -0.984, -0.487, 0.144, 0.679, 0.679, 0.783, 0.441, 0.16, -0.391, -0.276, 0.59, 0.296, 0.269, -1.128, -1.123, -1.075, -1.083, -0.954, -0.613, 0.044, 0.398, 0.398, 0.567, 0.036, -0.053, -0.451, -0.453, -0.23, 0.333, 0.641, -1.027, -0.989, -1.001, -0.953, -0.494, -0.51, -0.263, -0.06, -0.06, 0.139, -0.042, -0.052, -0.551, -0.454, -0.447, -0.264, 0.083, -0.569, -0.867, -0.084, -0.199, 0.111, -0.144, 0.027, -0.152, -0.152, -0.434, -0.018, -0.5, -0.941, -0.89, -0.698, -0.562, -0.517, -0.283, -0.231, -0.14, 0.098, 0.238, 0.336, -0.011, -0.221, -0.221, -0.309, -0.57, -0.954, -0.955, -1.137, -0.91, -0.992, -0.778, 0.092, 0.219, 0.443, 0.66, 0.919, 0.893, 0.503, -0.209, -0.209, -0.668, -0.678, -0.821, -0.865, -0.884, -1.024, -1.031, -0.915, 0.07, 0.57, 0.867, 1.866, 1.152, 1.308, 0.585, -0.169, -0.169, -0.534, -0.566, -0.805, -0.879, -0.976, -0.943, -0.934, -0.796, -0.014, 0.052, 1.561, 1.652, 1.328, 1.06, 0.784, -0.052, -0.052, -0.677, -0.652, -0.874, -0.966, -0.89, -0.831, -0.8, -0.757, -0.061, -0.748, 0.28, 1.593, 1.697, 1.074, 0.219, -0.27, -0.27, -0.721, -0.605, -0.689, -0.699, -0.691, -0.646, -0.673, -0.633, -0.11, 0.563, 1.383, 0.783, 0.994, 1.046, 0.217, -0.384, -0.384, -0.079, -0.567, -0.581, -0.603, -0.557, -0.506, -0.391, -0.436, -0.189, -0.12, 0.721, 0.699, -0.156, -0.061, -0.066, -0.015, -0.015, -0.571, -0.508, -0.409, -0.276, -0.38, -0.319, 0.122, -0.094, -0.622, -0.449, 0.103, 0.257, -0.192, 0.256, 0.166, -0.262, -0.262, -0.331, -0.086, -0.103, -0.147, -0.009, -0.181, -0.087, -0.256, -0.877, -0.355, -0.041, 0.217, 0.41, 0.646, 0.215, -0.435, -0.435, -0.155, 0.022, -0.159, -0.013, -0.169, -0.341, -0.415, -0.518, -0.994, 0.506, 0.143, 0.655, 0.838, 0.639, 0.549, -0.061, -0.061, -0.556, -0.285, -0.375, -0.272, -0.38, -0.677, -0.44, -0.302, -0.895, -0.904, -0.513, 0.387, 0.513, 0.457, 0.203, -0.23, -0.23, -0.283, -0.405, -0.311, -0.352, -0.38, -0.785, -0.44, -0.302),
evi=c(0.194, 0.729, 1.702, 0.823, 0.444, 0.94, 1.779, -0.051, -0.198, 1.785, 0.786, 0.826, 0.615, -0.644, 0.683, 0.458, 0.538, -0.438, 0.886, 0.527, 0.468, 0.787, 1.075, 1.469, 0.304, -1.303, -0.954, -0.868, -0.572, 1.357, 0.034, 0.379, 1.176, 1.173, -0.133, 0.732, 1.168, 0.536, -0.035, 1.109, 1.14, -0.87, -1.421, -1.28, -1.255, -0.994, 1.226, 1.119, -0.173, 0.121, 1.13, 0.489, 0.748, -0.19, 0.725, 0.449, -0.165, -0.211, 0.86, -0.91, -0.419, -0.248, -0.389, -0.8, -0.451, -0.349, 1.195, 0.806, 0.375, 0.551, -1.046, -0.653, 0.886, 1.03, 0.038, -1.702, -1.132, -1.318, -1.341, -1.061, -0.641, -0.051, -0.388, -0.709, -0.939, 0.29, 1.535, -0.26, -1.576, -0.566, 0.78, 0.846, 0.501, -0.601, -1.74, -1.427, -0.356, -0.481, -1.094, -0.362, -1.027, -0.534, 0.513, 0.044, 0.499, -1.052, -0.612, -1.068, 0.336, -0.453, -0.07, -0.235, -0.647, -0.947, -0.787, -0.73, -0.499, -0.18, -0.119, 0.667, 0.971, 0.637, 0.622, 0.219, 0.278, -0.345, -1.319, -0.615, -0.638, -1.439, -0.837, -0.865, -0.767, -0.526, -0.414, -0.429, 0.183, 0.145, 0.459, 0.656, 0.622, 0.76, -0.026, -1.132, -0.944, -1.103, -0.44, -0.518, -0.917, -0.852, -0.575, 2.294, 2.129, 1.429, 0.747, 0.823, 0.766, 1.226, 0.864, 0.32, -0.497, -0.382, -0.407, -0.569, -0.822, -0.577, -0.933, 1.072, 1.926, 1.139, 1.331, 1.131, 1.862, 1.999, 1.325, 1.168, 0.464, -0.76, 0.028, -0.48, -0.615, -0.346, 0.198, 0.305, 1.893, 2.297, 2.025, -0.336, 0.815, 0.843, 1.352, 1.079, 1.205, 1.081, -0.322, 0.502, -0.247, -0.176, -0.389, -1.049, -0.247, 0.907, 0.895, 1.882, 0.124, 0.805, 0.7, 0.363, 0.385, 0.642, 0.956, -0.821, -0.195, -0.354, -0.303, -0.183, -0.616, -0.889, -0.711, -0.534, -0.302, -0.496, -1.016, 0.645, 1.018, 0.772, 1.994, 0.204, -0.612, -0.388, 0.228, -0.846, -2.052, 2.091, -0.024, -0.775, -0.707, -0.732, -0.389, 0.486, 0.993, 0.867, 0.243, -0.345, -0.364, -0.373, 0.129, 0.826, 1.158, 2.484, 1.373, 1.478, -0.165, -0.824, -0.812, -3.326, -0.402, -0.03, -0.204, -0.837, -0.505, -0.518, -0.687, -0.327, -0.127, 0.983, 1.818, 1.867, 2.279, 0.51, 0.014, -0.692, -0.818, -0.797, -1.401, -1.315, -0.695, -0.224, -0.491, -0.754, 0.369, 1.368, 2.196, 2.258, 1.38, 1.994, 0.812, 0.062, 0.332, -2.093, -2.259, 0.266, -0.671, -0.831, -0.807, -1.752, -0.529, 0.643, 1.641, 1.637, 2.063, 1.979, 1.853, 0.258, 0.24, 0.209, -0.601, -0.763, -0.6, -0.13, -0.035, -0.89, -0.907, -0.877, 1.179, 2.137, 1.957, 1.72, 2.137, 2.082, 1.426, 0.637, 0.335, -1.417, -0.76, -0.164, 0.326, -0.006, -0.813, -0.69, -0.367, 1.667, 1.981, 1.994, 2.291, 2.092, 1.618, 2.132, 0.585, 0.425, -0.95, -0.763, -0.83, 0.299, -0.37, -0.816, -0.241, 1.278, 0.096, 1.164, -0.308, 0.265, 1.079, 1.761, 1.73, 1.398, 0.48, -2.584, 0.382, 0.031, -0.018, -0.582, -0.85, -0.687, -0.778, -1.183, -0.968, 0.658, 0.514, 1.454, 1.545, 1.628, 0.106, -0.745, -0.853, -0.583, -0.128, -0.273, -0.512, -0.957, -0.77, -1.111, -0.945, -1.005, -0.508, 0.806, 0.602, 0.038, -0.041, 0.2, 0.18, -0.893, -0.576, -0.374, -0.48, -1.095, -0.837, -0.904, -1.031, -0.904, -0.904, -1.129, -1.187, -0.932, -0.233, 0.373, 0.422, -0.76, -0.373, -0.293, -0.385, -0.232, -0.779, -0.576, -1.755, -0.971, -1.068, -1.128, -1.054, -0.893, -0.876, -0.672, -0.44, -0.696, -0.531, -1.095, -0.818, -0.273, 0.042, -0.696, -0.677, 0.022, 0.063, -0.457, -0.769, -1.108, -0.84, -0.674, -0.146, -0.503, -0.115, 0.369, -0.216, -0.573, -0.649, 0.367, -0.536, -0.297, -0.313, -0.715, -0.806, -0.57, -0.721, -0.52, 0.858, 1.122, 0.565, -0.833, -3.578, 0.06, 0.244, -0.46, -0.138, 0.572, -0.278, -1.297, -0.529, -0.595, -0.65, -0.546, -0.266, -0.259, -0.505, -1.595, -3.4, -2.894),
ph1=c(-1.109, -1.957, -1.46, -1.431, -1.577, -0.67, -0.962, 0.091, -0.026, -1.021, -0.231, -0.904, -0.582, 0.852, 0.852, 0.852, 0.413, -0.962, -1.606, -1.255, -2.045, -2.074, -1.46, 0.237, 0.325, 0.764, 0.676, 0.735, 0.852, 0.266, 0.091, 0.764, 0.032, 0.793, -0.524, -0.582, -1.46, -1.811, -1.431, 0.179, -0.202, 0.705, 0.852, 0.852, 0.852, 0.852, 0.179, -1.167, 0.266, -0.904, 0.705, -1.021, -1.255, -0.67, -0.085, -0.582, 0.237, 0.501, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.705, 0.559, -1.05, -0.377, -1.665, -1.518, 0.062, 0.852, -0.026, -0.407, -0.055, 0.325, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, -0.085, -0.202, 0.266, -1.723, -0.172, -0.728, 0.852, 0.852, 0.588, -0.026, -0.728, -0.816, 0.735, 0.852, 0.852, 0.852, 0.822, 0.53, 0.852, 0.53, -1.723, -0.231, -1.079, 0.266, 0.852, 0.735, 0.442, 0.852, 0.091, 0.003, 0.822, 0.852, 0.852, 0.852, 0.852, 0.559, 0.735, -2.074, -1.401, -0.699, -0.114, 0.208, -0.407, -0.26, 0.53, 0.442, 0.852, 0.852, 0.793, 0.793, 0.764, 0.325, 0.618, 0.032, -1.84, -0.114, 0.12, -1.752, -1.372, -0.202, 0.471, 0.559, 0.296, 0.647, 0.852, 0.852, 0.852, 0.53, 0.413, 0.325, -1.489, -2.074, -1.05, -1.197, -1.197, 0.705, -0.816, -1.021, 0.53, 0.793, 0.852, 0.852, 0.618, 0.413, 0.266, 0.588, -0.845, -1.197, -1.957, -1.431, -0.553, 0.559, -0.933, -1.84, -1.723, 0.618, 0.852, 0.764, 0.559, 0.647, 0.442, 0.53, -0.67, -1.138, -1.197, -0.582, -0.436, -0.67, -1.431, -1.928, -1.05, 0.149, 0.647, 0.852, 0.559, 0.618, 0.588, 0.647, 0.735, 0.413, -0.465, -0.699, 0.032, -1.226, -1.957, -1.928, -1.899, -0.407, -1.635, 0.764, 0.647, 0.501, 0.559, 0.354, 0.266, 0.822, 0.852, 0.852, 0.852, -0.787, -2.074, -1.84, -0.758, -1.255, -1.548, -0.202, 0.559, 0.793, 0.618, 0.705, 0.559, 0.413, 0.266, 0.852, 0.852, 0.852, -2.045, -2.074, -1.957, -1.489, -2.045, -1.109, 0.442, 0.852, 0.852, 0.852, -0.026, -1.431, -1.05, -1.197, -1.138, 0.442, 0.588, -2.074, -2.045, -1.723, -0.553, 0.354, 0.354, 0.618, 0.852, 0.852, 0.822, -0.143, -1.255, -1.05, -2.074, -2.074, -1.635, 0.208, 0.354, 0.208, 0.501, 0.062, 0.852, 0.793, 0.852, 0.852, 0.852, 0.354, -1.46, -0.348, -1.635, -2.074, -2.074, -2.074, -2.045, 0.618, 0.413, -0.553, 0.676, 0.852, 0.852, 0.852, 0.852, 0.852, -0.114, -1.782, -0.582, -2.074, -2.074, -2.074, -2.074, -2.074, 0.501, 0.852, 0.705, 0.676, 0.852, 0.852, 0.852, 0.852, 0.822, -1.255, -1.314, -1.869, -2.074, -2.074, -2.074, -2.074, -1.665, 0.676, 0.618, 0.705, 0.413, 0.852, 0.852, 0.852, 0.588, -0.933, -2.074, -1.401, -1.84, -2.074, -2.074, -2.074, -1.079, 0.676, 0.237, 0.735, 0.676, 0.647, 0.735, 0.852, 0.852, -0.348, -1.987, -1.635, -1.021, -0.728, -2.074, -2.074, -1.84, -0.289, 0.208, -0.816, 0.618, 0.588, 0.852, 0.559, 0.852, 0.852, 0.852, 0.822, 0.852, 0.852, 0.325, -1.635, -0.319, 0.354, -0.085, 0.413, -0.348, 0.471, 0.852, 0.705, 0.442, 0.793, 0.852, 0.852, 0.852, 0.852, 0.793, -0.055, 0.705, 0.852, 0.852, 0.852, 0.852, 0.852, 0.354, 0.53, 0.852, 0.471, 0.588, 0.384, 0.647, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.647, 0.764, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.442, 0.559, 0.735, 0.822, 0.618, 0.852, 0.852, 0.237, 0.559, 0.647, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.559, 0.852, 0.735, 0.413, 0.471, 0.442, 0.442, 0.647, 0.588, 0.852, 0.471, 0.647, 0.793, 0.735, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.852, 0.676, 0.852, 0.852, 0.852, 0.852, 0.852, 0.793, 0.852, 0.852, -1.314, -0.172, 0.296, 0.442, -1.723),
num=c(3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 5, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 3),
adj=c(2, 18, 19, 1, 3, 18, 19, 20, 2, 4, 19, 20, 21, 3, 5, 20, 21, 22, 4, 6, 21, 22, 23, 5, 7, 22, 23, 24, 6, 8, 23, 24, 25, 7, 9, 24, 25, 26, 8, 10, 25, 26, 27, 9, 11, 26, 27, 28, 10, 12, 27, 28, 29, 11, 13, 28, 29, 30, 12, 14, 29, 30, 31, 13, 15, 30, 31, 32, 14, 16, 31, 32, 33, 15, 17, 32, 33, 34, 16, 33, 34, 1, 2, 19, 35, 36, 1, 2, 3, 18, 20, 35, 36, 37, 2, 3, 4, 19, 21, 36, 37, 38, 3, 4, 5, 20, 22, 37, 38, 39, 4, 5, 6, 21, 23, 38, 39, 40, 5, 6, 7, 22, 24, 39, 40, 41, 6, 7, 8, 23, 25, 40, 41, 42, 7, 8, 9, 24, 26, 41, 42, 43, 8, 9, 10, 25, 27, 42, 43, 44, 9, 10, 11, 26, 28, 43, 44, 45, 10, 11, 12, 27, 29, 44, 45, 46, 11, 12, 13, 28, 30, 45, 46, 47, 12, 13, 14, 29, 31, 46, 47, 48, 13, 14, 15, 30, 32, 47, 48, 49, 14, 15, 16, 31, 33, 48, 49, 50, 15, 16, 17, 32, 34, 49, 50, 51, 16, 17, 33, 50, 51, 18, 19, 36, 52, 53, 18, 19, 20, 35, 37, 52, 53, 54, 19, 20, 21, 36, 38, 53, 54, 55, 20, 21, 22, 37, 39, 54, 55, 56, 21, 22, 23, 38, 40, 55, 56, 57, 22, 23, 24, 39, 41, 56, 57, 58, 23, 24, 25, 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sumNumNeigh=3542)