test_dat <- list(M = 1500L, J = 5L, T = 3, E = 1, G = 3L, N = c(65, 106, 129), ii = c(276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84, 276, 220, 179, 65, 82, 68, 284, 116, 37, 90, 122, 251, 145, 261, 146, 6, 27, 204, 254, 245, 41, 218, 8, 268, 192, 74, 104, 281, 275, 72, 95, 207, 45, 196, 131, 297, 290, 260, 248, 157, 61, 274, 26, 81, 98, 165, 38, 124, 206, 88, 228, 215, 269, 200, 278, 85, 174, 106, 135, 93, 136, 293, 292, 143, 92, 32, 216, 151, 194, 57, 140, 28, 12, 159, 175, 52, 3, 102, 101, 77, 253, 182, 212, 31, 16, 195, 4, 189, 256, 172, 158, 128, 298, 291, 142, 240, 229, 210, 282, 236, 223, 103, 141, 44, 71, 9, 54, 79, 138, 277, 10, 267, 91, 238, 266, 86, 18, 123, 111, 19, 1, 247, 163, 34, 14, 96, 299, 205, 271, 201, 241, 29, 184, 25, 137, 66, 49, 147, 198, 87, 21, 188, 213, 150, 134, 51, 176, 237, 127, 243, 255, 202, 160, 7, 148, 296, 180, 193, 120, 185, 20, 125, 272, 113, 149, 139, 129, 15, 259, 226, 119, 263, 181, 230, 94, 42, 170, 80, 64, 48, 89, 155, 109, 70, 265, 222, 264, 203, 270, 35, 249, 117, 242, 279, 126, 258, 183, 285, 233, 110, 288, 289, 99, 171, 191, 50, 63, 5, 60, 177, 208, 133, 114, 199, 286, 283, 67, 168, 78, 132, 153, 56, 169, 40, 187, 190, 262, 224, 162, 250, 178, 115, 173, 287, 130, 39, 2, 76, 217, 22, 273, 152, 161, 221, 167, 69, 100, 219, 246, 53, 47, 97, 55, 154, 23, 107, 43, 46, 209, 294, 166, 58, 24, 234, 244, 17, 108, 197, 300, 105, 227, 112, 118, 83, 156, 164, 36, 73, 252, 59, 211, 75, 144, 33, 231, 214, 13, 295, 186, 280, 11, 257, 225, 239, 62, 121, 30, 232, 235, 84), jj = 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 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, 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, 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, 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, 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, 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, 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, 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, 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), gg = c(2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 3, 1, 3, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 1, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 2, 2, 3, 3, 3, 2, 3, 3, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 3, 2, 2, 3, 3, 3, 2, 1, 2, 2, 1, 1, 3, 3, 2, 2, 3, 3, 3, 3, 3, 2, 3, 2, 1, 3, 1, 1, 1, 3, 1, 2, 1, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 2, 1, 1, 3, 1, 2, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 2, 2, 2, 2, 3, 1, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 3, 2, 3, 2, 1, 1, 1, 3, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 2, 3, 3, 2, 1, 2, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 3, 3, 1, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 1, 3, 1, 2, 3, 2, 3, 2, 1, 3, 2, 3, 3, 2, 2, 2, 3, 1, 3, 3, 3, 3, 3, 1, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 3, 2, 3, 3, 3, 3, 2, 3, 3, 1, 2, 3, 3, 1, 3, 2, 1, 1, 1, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 3, 3, 3, 3, 3, 2, 2), g_all = c(116, 122, 251, 268, 72, 274, 215, 200, 106, 293, 57, 182, 31, 128, 142, 240, 138, 10, 267, 91, 266, 18, 247, 163, 271, 201, 29, 150, 51, 237, 20, 149, 139, 64, 48, 89, 109, 233, 288, 289, 99, 63, 5, 60, 133, 114, 199, 286, 78, 250, 115, 76, 100, 55, 154, 23, 43, 24, 234, 83, 73, 211, 75, 144, 280, 276, 179, 68, 90, 145, 261, 245, 8, 192, 74, 104, 207, 131, 290, 157, 61, 26, 81, 124, 174, 135, 93, 292, 143, 92, 32, 194, 140, 28, 12, 101, 253, 195, 4, 158, 298, 291, 282, 236, 9, 79, 86, 205, 184, 25, 137, 147, 198, 188, 213, 134, 127, 255, 7, 296, 180, 193, 120, 272, 129, 15, 259, 226, 181, 42, 80, 70, 222, 203, 35, 117, 126, 285, 110, 191, 177, 208, 283, 153, 56, 40, 187, 224, 162, 173, 130, 2, 22, 161, 221, 167, 209, 166, 17, 227, 156, 59, 33, 231, 13, 295, 186, 257, 225, 235, 84, 220, 65, 82, 284, 37, 146, 6, 27, 204, 254, 41, 218, 281, 275, 95, 45, 196, 297, 260, 248, 98, 165, 38, 206, 88, 228, 269, 278, 85, 136, 216, 151, 159, 175, 52, 3, 102, 77, 212, 16, 189, 256, 172, 229, 210, 223, 103, 141, 44, 71, 54, 277, 238, 123, 111, 19, 1, 34, 14, 96, 299, 241, 66, 49, 87, 21, 176, 243, 202, 160, 148, 185, 125, 113, 119, 263, 230, 94, 170, 155, 265, 264, 270, 249, 242, 279, 258, 183, 171, 50, 67, 168, 132, 169, 190, 262, 178, 287, 39, 217, 273, 152, 69, 219, 246, 53, 47, 97, 107, 46, 294, 58, 244, 108, 197, 300, 105, 112, 118, 164, 36, 252, 214, 11, 239, 62, 121, 30, 232), y = c(4, 3, 1, 2, 2, 2, 4, 4, 3, 2, 4, 1, 3, 2, 3, 2, 1, 2, 4, 4, 1, 3, 1, 2, 4, 2, 3, 4, 1, 3, 3, 3, 3, 2, 4, 4, 4, 4, 3, 3, 4, 2, 1, 2, 2, 3, 3, 3, 4, 2, 1, 4, 4, 4, 3, 4, 3, 2, 2, 3, 3, 4, 4, 2, 1, 2, 3, 3, 2, 3, 3, 2, 3, 2, 3, 3, 2, 2, 1, 4, 4, 2, 3, 2, 3, 3, 3, 4, 3, 2, 4, 4, 4, 4, 2, 3, 4, 1, 3, 4, 4, 3, 3, 2, 2, 1, 4, 2, 3, 3, 1, 3, 2, 3, 2, 2, 2, 4, 3, 4, 1, 4, 4, 2, 1, 3, 4, 3, 4, 4, 3, 2, 2, 1, 2, 3, 3, 4, 2, 2, 4, 3, 1, 3, 3, 3, 4, 1, 4, 2, 3, 2, 4, 1, 4, 4, 3, 2, 2, 3, 3, 3, 4, 3, 3, 2, 4, 2, 4, 4, 2, 3, 4, 2, 4, 2, 3, 2, 2, 2, 2, 3, 3, 2, 3, 4, 3, 2, 3, 3, 4, 3, 3, 4, 3, 4, 4, 4, 3, 2, 4, 4, 2, 2, 4, 3, 2, 3, 4, 4, 3, 1, 3, 2, 3, 3, 1, 3, 2, 2, 3, 3, 3, 1, 3, 4, 2, 4, 4, 4, 4, 2, 3, 3, 4, 3, 1, 4, 3, 3, 4, 4, 4, 4, 3, 2, 2, 3, 3, 4, 1, 2, 2, 3, 1, 4, 2, 2, 4, 3, 2, 3, 3, 3, 3, 1, 2, 3, 4, 3, 3, 1, 2, 3, 4, 2, 3, 4, 3, 2, 1, 4, 3, 3, 4, 3, 3, 4, 3, 3, 2, 4, 4, 1, 3, 3, 4, 4, 3, 3, 3, 4, 3, 3, 2, 1, 4, 3, 2, 3, 3, 4, 3, 4, 4, 2, 1, 4, 3, 3, 1, 4, 2, 3, 4, 3, 3, 2, 4, 3, 2, 4, 4, 3, 4, 4, 4, 4, 4, 3, 3, 4, 2, 4, 4, 3, 3, 3, 4, 1, 4, 3, 4, 3, 3, 4, 3, 3, 2, 3, 1, 4, 4, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 2, 1, 1, 4, 2, 3, 2, 2, 3, 3, 4, 4, 4, 3, 4, 4, 4, 2, 4, 3, 2, 4, 4, 4, 2, 3, 1, 1, 3, 4, 4, 3, 4, 3, 3, 3, 2, 4, 2, 3, 3, 3, 4, 1, 4, 3, 3, 1, 4, 4, 3, 4, 4, 3, 3, 4, 2, 3, 2, 1, 3, 4, 3, 3, 4, 4, 3, 3, 3, 4, 3, 4, 4, 4, 3, 3, 2, 4, 4, 2, 4, 4, 3, 3, 3, 4, 4, 3, 3, 3, 2, 4, 4, 2, 2, 4, 2, 1, 3, 4, 4, 3, 2, 2, 3, 3, 3, 2, 4, 3, 4, 4, 2, 4, 3, 4, 4, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 3, 2, 3, 3, 4, 3, 4, 3, 2, 2, 4, 4, 2, 4, 3, 4, 4, 4, 4, 4, 3, 4, 3, 4, 2, 2, 4, 4, 3, 4, 4, 4, 4, 4, 2, 4, 4, 4, 3, 2, 3, 3, 3, 2, 2, 2, 4, 4, 4, 4, 3, 3, 4, 4, 2, 3, 4, 4, 3, 3, 4, 3, 4, 3, 3, 2, 3, 4, 3, 2, 4, 3, 4, 4, 2, 3, 4, 3, 3, 2, 4, 4, 3, 4, 4, 4, 3, 4, 4, 2, 4, 2, 1, 3, 2, 1, 1, 3, 2, 2, 2, 3, 3, 2, 1, 2, 4, 3, 4, 1, 3, 2, 4, 4, 3, 3, 2, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 2, 1, 2, 3, 2, 3, 3, 3, 2, 1, 2, 3, 1, 4, 3, 4, 4, 1, 2, 3, 4, 2, 4, 3, 2, 2, 2, 3, 4, 4, 3, 1, 4, 3, 2, 1, 2, 2, 3, 3, 1, 2, 1, 3, 2, 2, 3, 4, 4, 3, 4, 4, 4, 4, 1, 1, 2, 3, 4, 4, 2, 3, 4, 3, 1, 4, 3, 1, 4, 2, 3, 2, 1, 2, 2, 3, 2, 4, 1, 1, 2, 2, 2, 4, 2, 4, 4, 3, 1, 2, 2, 2, 1, 1, 1, 3, 4, 2, 1, 3, 4, 3, 1, 1, 3, 4, 1, 4, 2, 3, 3, 4, 1, 3, 4, 3, 1, 2, 3, 3, 2, 4, 4, 1, 3, 4, 3, 4, 4, 4, 2, 3, 4, 4, 2, 4, 3, 1, 3, 1, 2, 3, 4, 2, 4, 3, 4, 4, 3, 4, 1, 2, 2, 3, 4, 1, 4, 4, 3, 2, 4, 3, 4, 4, 1, 2, 2, 4, 4, 4, 1, 1, 3, 4, 4, 2, 2, 2, 2, 1, 1, 3, 1, 3, 4, 1, 4, 4, 4, 4, 2, 3, 3, 3, 3, 1, 4, 3, 2, 4, 1, 4, 4, 3, 4, 4, 3, 2, 4, 1, 4, 2, 2, 3, 3, 2, 3, 4, 4, 3, 2, 3, 4, 2, 1, 3, 2, 4, 2, 3, 4, 3, 3, 3, 2, 3, 2, 2, 3, 2, 4, 3, 2, 1, 2, 2, 4, 4, 3, 2, 4, 4, 3, 4, 2, 2, 3, 4, 4, 2, 4, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 3, 2, 3, 2, 3, 2, 1, 4, 1, 3, 4, 3, 1, 3, 2, 2, 2, 3, 2, 2, 2, 4, 2, 4, 3, 1, 2, 1, 1, 2, 3, 2, 3, 2, 2, 4, 2, 1, 3, 3, 4, 2, 4, 1, 1, 1, 1, 3, 4, 2, 1, 2, 3, 1, 1, 2, 3, 2, 1, 4, 4, 2, 1, 3, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 1, 4, 2, 4, 2, 3, 1, 2, 3, 4, 1, 3, 4, 4, 2, 4, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 2, 3, 1, 1, 4, 1, 2, 1, 2, 4, 3, 3, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 3, 3, 1, 1, 1, 3, 3, 1, 2, 3, 4, 3, 3, 1, 2, 4, 3, 1, 1, 2, 2, 4, 4, 4, 1, 2, 4, 1, 4, 4, 2, 3, 4, 3, 2, 2, 1, 1, 1, 1, 3, 3, 2, 2, 3, 4, 1, 2, 3, 2, 4, 2, 1, 4, 2, 4, 1, 1, 3, 1, 3, 2, 3, 2, 3, 1, 1, 2, 1, 3, 4, 1, 1, 2, 3, 2, 1, 3, 1, 2, 3, 1, 3, 1, 3, 4, 2, 4, 4, 2, 4, 1, 2, 4, 3, 3, 1, 4, 1, 1, 4, 1, 2, 3, 1, 3, 4, 3, 4, 1, 2, 4, 1, 1, 3, 1, 2, 2, 4, 4, 2, 1, 1, 1, 3, 1, 4, 2, 4, 1, 2, 4, 1, 1, 1, 2, 3, 1, 3, 3, 3, 4, 3, 1, 2, 2, 1, 4, 1, 1, 2, 3, 4, 1, 3, 1, 3, 2, 4, 1, 4, 4, 2, 2, 4, 4, 4, 3, 3, 3, 3, 2, 3, 2, 3, 2, 2, 4, 4, 4, 2, 2, 2, 4, 4, 4, 2, 3, 3, 3, 4, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 1, 3, 3, 4, 3, 3, 4, 4, 2, 4, 3, 4, 4, 4, 4, 3, 2, 3, 4, 1, 4, 4, 4, 3, 2, 3, 3, 2, 3, 1, 1, 2, 4, 4, 4, 3, 2, 3, 1, 3, 2, 2, 3, 2, 2, 4, 4, 4, 3, 3, 4, 4, 4, 3, 2, 3, 2, 4, 4, 4, 3, 3, 4, 3, 2, 4, 2, 3, 3, 3, 3, 3, 2, 3, 2, 2, 4, 4, 3, 1, 4, 2, 4, 1, 4, 4, 4, 4, 4, 3, 3, 4, 1, 4, 2, 3, 3, 4, 2, 4, 3, 3, 3, 1, 3, 4, 2, 3, 4, 4, 4, 4, 1, 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 2, 2, 3, 3, 4, 4, 3, 3, 4, 3, 3, 2, 4, 3, 2, 3, 3, 3, 3, 2, 3, 4, 3, 3, 4, 3, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 4, 4, 4, 4, 4, 1, 2, 4, 4, 4, 2, 2, 4, 4, 3, 3, 3, 3, 2, 4, 3, 3, 1, 3, 4, 4, 4, 4, 4, 4, 2, 4, 4, 4, 4, 2, 4, 4, 2, 4, 3, 4, 4, 3, 2, 4, 4, 4, 4, 2, 2, 2, 4, 3, 3, 3, 4, 4, 4, 2, 4, 2, 4, 4, 2, 1, 3, 4, 3, 3, 4, 3, 3, 4, 2, 2, 4, 3, 4, 1, 3, 3, 2, 4, 3, 2, 4, 4, 3, 3, 4, 4, 3, 4, 4, 3, 3, 4, 4), obs_corr = structure(c(1, 1, 1, 0.51900000000000002, 0.626, 0.38700000000000001, 0.23699999999999999, 0.67900000000000005, 0.22800000000000001, 0.23999999999999999, 0.70999999999999996, 0.28199999999999997, 0.59999999999999998, 0.66000000000000003, 0.45500000000000002, 0.51900000000000002, 0.626, 0.38700000000000001, 1, 1, 1, 0.39400000000000002, 0.58199999999999996, 0.22700000000000001, 0.22700000000000001, 0.53900000000000003, 0.30599999999999999, 0.53700000000000003, 0.52600000000000002, 0.72199999999999998, 0.23699999999999999, 0.67900000000000005, 0.22800000000000001, 0.39400000000000002, 0.58199999999999996, 0.22700000000000001, 1, 1, 1, 0.49099999999999999, 0.68000000000000005, 0.52900000000000003, 0.46899999999999997, 0.56999999999999995, 0.44600000000000001, 0.23999999999999999, 0.70999999999999996, 0.28199999999999997, 0.22700000000000001, 0.53900000000000003, 0.30599999999999999, 0.49099999999999999, 0.68000000000000005, 0.52900000000000003, 1, 1, 1, 0.49299999999999999, 0.57199999999999995, 0.42899999999999999, 0.59999999999999998, 0.66000000000000003, 0.45500000000000002, 0.53700000000000003, 0.52600000000000002, 0.72199999999999998, 0.46899999999999997, 0.56999999999999995, 0.44600000000000001, 0.49299999999999999, 0.57199999999999995, 0.42899999999999999, 1, 1, 1), .Dim = c(3L, 5L, 5L)))