1R = QQ[x1, x2, x3, x4, x5, x6, x7, x8]; 2p = 3 -x2^2*x3^2*x4*x5*x6*x7*x8 + 4 x2^2*x3^2*x4*x5*x6*x7 + 5 x2^2*x3^2*x4*x5*x6*x8 + 6 -x2^2*x3^2*x4*x5*x6 + 7 x2^2*x3^2*x4*x5*x7*x8 + 8 -x2^2*x3^2*x4*x5*x7 + 9 -x2^2*x3^2*x4*x5*x8 + 10 x2^2*x3^2*x4*x5 + 11 x2^2*x3^2*x4*x6*x7*x8 + 12 -x2^2*x3^2*x4*x6*x7 + 13 -x2^2*x3^2*x4*x6*x8 + 14 x2^2*x3^2*x4*x6 + 15 -x2^2*x3^2*x4*x7*x8 + 16 x2^2*x3^2*x4*x7 + 17 x2^2*x3^2*x4*x8 + 18 -x2^2*x3^2*x4 + 19 x2^2*x3^2*x5*x6*x7*x8 + 20 -x2^2*x3^2*x5*x6*x7 + 21 -x2^2*x3^2*x5*x6*x8 + 22 x2^2*x3^2*x5*x6 + 23 -x2^2*x3^2*x5*x7*x8 + 24 x2^2*x3^2*x5*x7 + 25 x2^2*x3^2*x5*x8 + 26 -x2^2*x3^2*x5 + 27 -x2^2*x3^2*x6*x7*x8 + 28 x2^2*x3^2*x6*x7 + 29 x2^2*x3^2*x6*x8 + 30 -x2^2*x3^2*x6 + 31 x2^2*x3^2*x7*x8 + 32 -x2^2*x3^2*x7 + 33 -x2^2*x3^2*x8 + 34 x2^2*x3^2 + 35 x2^2*x4*x5*x6*x7*x8 + 36 -x2^2*x4*x5*x6*x7 + 37 -x2^2*x4*x5*x6*x8 + 38 x2^2*x4*x5*x6 + 39 -x2^2*x4*x5*x7*x8 + 40 x2^2*x4*x5*x7 + 41 x2^2*x4*x5*x8 + 42 -x2^2*x4*x5 + 43 -x2^2*x4*x6*x7*x8 + 44 x2^2*x4*x6*x7 + 45 x2^2*x4*x6*x8 + 46 -x2^2*x4*x6 + 47 x2^2*x4*x7*x8 + 48 -x2^2*x4*x7 + 49 -x2^2*x4*x8 + 50 x2^2*x4 + 51 -x2^2*x5*x6*x7*x8 + 52 x2^2*x5*x6*x7 + 53 x2^2*x5*x6*x8 + 54 -x2^2*x5*x6 + 55 x2^2*x5*x7*x8 + 56 -x2^2*x5*x7 + 57 -x2^2*x5*x8 + 58 x2^2*x5 + 59 x2^2*x6*x7*x8 + 60 -x2^2*x6*x7 + 61 -x2^2*x6*x8 + 62 x2^2*x6 + 63 -x2^2*x7*x8 + 64 x2^2*x7 + 65 x2^2*x8 + 66 -x2^2 + 67 -x2*x3^3*x4*x5^2*x6*x7*x8 + 68 x2*x3^3*x4*x5^2*x6*x7 + 69 x2*x3^3*x4*x5^2*x6*x8 + 70 -x2*x3^3*x4*x5^2*x6 + 71 x2*x3^3*x4*x5^2*x7*x8 + 72 -x2*x3^3*x4*x5^2*x7 + 73 -x2*x3^3*x4*x5^2*x8 + 74 x2*x3^3*x4*x5^2 + 75 x2*x3^3*x4*x6*x7*x8 + 76 -x2*x3^3*x4*x6*x7 + 77 -x2*x3^3*x4*x6*x8 + 78 x2*x3^3*x4*x6 + 79 -x2*x3^3*x4*x7*x8 + 80 x2*x3^3*x4*x7 + 81 x2*x3^3*x4*x8 + 82 -x2*x3^3*x4 + 83 x2*x3^3*x5^2*x6*x7*x8 + 84 -x2*x3^3*x5^2*x6*x7 + 85 -x2*x3^3*x5^2*x6*x8 + 86 x2*x3^3*x5^2*x6 + 87 -x2*x3^3*x5^2*x7*x8 + 88 x2*x3^3*x5^2*x7 + 89 x2*x3^3*x5^2*x8 + 90 -x2*x3^3*x5^2 + 91 -x2*x3^3*x6*x7*x8 + 92 x2*x3^3*x6*x7 + 93 x2*x3^3*x6*x8 + 94 -x2*x3^3*x6 + 95 x2*x3^3*x7*x8 + 96 -x2*x3^3*x7 + 97 -x2*x3^3*x8 + 98 x2*x3^3 + 99 -x2*x3^2*x4*x5*x6*x7^2*x8 + 100 x2*x3^2*x4*x5*x6*x7^2 + 101 2*x2*x3^2*x4*x5*x6*x7*x8 + 102 -2*x2*x3^2*x4*x5*x6*x7 + 103 -x2*x3^2*x4*x5*x6*x8 + 104 x2*x3^2*x4*x5*x6 + 105 x2*x3^2*x4*x5*x7^2*x8 + 106 -x2*x3^2*x4*x5*x7^2 + 107 -2*x2*x3^2*x4*x5*x7*x8 + 108 2*x2*x3^2*x4*x5*x7 + 109 x2*x3^2*x4*x5*x8 + 110 -x2*x3^2*x4*x5 + 111 x2*x3^2*x4*x6*x7^2*x8 + 112 -x2*x3^2*x4*x6*x7^2 + 113 -2*x2*x3^2*x4*x6*x7*x8 + 114 2*x2*x3^2*x4*x6*x7 + 115 x2*x3^2*x4*x6*x8 + 116 -x2*x3^2*x4*x6 + 117 -x2*x3^2*x4*x7^2*x8 + 118 x2*x3^2*x4*x7^2 + 119 2*x2*x3^2*x4*x7*x8 + 120 -2*x2*x3^2*x4*x7 + 121 -x2*x3^2*x4*x8 + 122 x2*x3^2*x4 + 123 x2*x3^2*x5*x6*x7^2*x8 + 124 -x2*x3^2*x5*x6*x7^2 + 125 -2*x2*x3^2*x5*x6*x7*x8 + 126 2*x2*x3^2*x5*x6*x7 + 127 x2*x3^2*x5*x6*x8 + 128 -x2*x3^2*x5*x6 + 129 -x2*x3^2*x5*x7^2*x8 + 130 x2*x3^2*x5*x7^2 + 131 2*x2*x3^2*x5*x7*x8 + 132 -2*x2*x3^2*x5*x7 + 133 -x2*x3^2*x5*x8 + 134 x2*x3^2*x5 + 135 -x2*x3^2*x6*x7^2*x8 + 136 x2*x3^2*x6*x7^2 + 137 2*x2*x3^2*x6*x7*x8 + 138 -2*x2*x3^2*x6*x7 + 139 -x2*x3^2*x6*x8 + 140 x2*x3^2*x6 + 141 x2*x3^2*x7^2*x8 + 142 -x2*x3^2*x7^2 + 143 -2*x2*x3^2*x7*x8 + 144 2*x2*x3^2*x7 + 145 x2*x3^2*x8 + 146 -x2*x3^2 + 147 -x2*x3*x4*x5^3*x6*x7*x8 + 148 x2*x3*x4*x5^3*x6*x7 + 149 x2*x3*x4*x5^3*x6*x8 + 150 -x2*x3*x4*x5^3*x6 + 151 x2*x3*x4*x5^3*x7*x8 + 152 -x2*x3*x4*x5^3*x7 + 153 -x2*x3*x4*x5^3*x8 + 154 x2*x3*x4*x5^3 + 155 x2*x3*x4*x5^2*x6*x7*x8 + 156 -x2*x3*x4*x5^2*x6*x7 + 157 -x2*x3*x4*x5^2*x6*x8 + 158 x2*x3*x4*x5^2*x6 + 159 -x2*x3*x4*x5^2*x7*x8 + 160 x2*x3*x4*x5^2*x7 + 161 x2*x3*x4*x5^2*x8 + 162 -x2*x3*x4*x5^2 + 163 -x2*x3*x4*x5*x6^2*x7*x8 + 164 x2*x3*x4*x5*x6^2*x7 + 165 x2*x3*x4*x5*x6^2*x8 + 166 -x2*x3*x4*x5*x6^2 + 167 x2*x3*x4*x5*x6*x7*x8 + 168 -x2*x3*x4*x5*x6*x7 + 169 -x2*x3*x4*x5*x6*x8 + 170 x2*x3*x4*x5*x6 + 171 x2*x3*x4*x6^2*x7*x8 + 172 -x2*x3*x4*x6^2*x7 + 173 -x2*x3*x4*x6^2*x8 + 174 x2*x3*x4*x6^2 + 175 -x2*x3*x4*x6*x7*x8 + 176 x2*x3*x4*x6*x7 + 177 x2*x3*x4*x6*x8 + 178 -x2*x3*x4*x6 + 179 x2*x3*x5^3*x6*x7*x8 + 180 -x2*x3*x5^3*x6*x7 + 181 -x2*x3*x5^3*x6*x8 + 182 x2*x3*x5^3*x6 + 183 -x2*x3*x5^3*x7*x8 + 184 x2*x3*x5^3*x7 + 185 x2*x3*x5^3*x8 + 186 -x2*x3*x5^3 + 187 -x2*x3*x5^2*x6*x7*x8 + 188 x2*x3*x5^2*x6*x7 + 189 x2*x3*x5^2*x6*x8 + 190 -x2*x3*x5^2*x6 + 191 x2*x3*x5^2*x7*x8 + 192 -x2*x3*x5^2*x7 + 193 -x2*x3*x5^2*x8 + 194 x2*x3*x5^2 + 195 x2*x3*x5*x6^2*x7*x8 + 196 -x2*x3*x5*x6^2*x7 + 197 -x2*x3*x5*x6^2*x8 + 198 x2*x3*x5*x6^2 + 199 -x2*x3*x5*x6*x7*x8 + 200 x2*x3*x5*x6*x7 + 201 x2*x3*x5*x6*x8 + 202 -x2*x3*x5*x6 + 203 -x2*x3*x6^2*x7*x8 + 204 x2*x3*x6^2*x7 + 205 x2*x3*x6^2*x8 + 206 -x2*x3*x6^2 + 207 x2*x3*x6*x7*x8 + 208 -x2*x3*x6*x7 + 209 -x2*x3*x6*x8 + 210 x2*x3*x6 + 211 x2*x4*x5^3*x6*x7*x8 + 212 -x2*x4*x5^3*x6*x7 + 213 -x2*x4*x5^3*x6*x8 + 214 x2*x4*x5^3*x6 + 215 -x2*x4*x5^3*x7*x8 + 216 x2*x4*x5^3*x7 + 217 x2*x4*x5^3*x8 + 218 -x2*x4*x5^3 + 219 x2*x4*x5*x6^2*x7*x8 + 220 -x2*x4*x5*x6^2*x7 + 221 -x2*x4*x5*x6^2*x8 + 222 x2*x4*x5*x6^2 + 223 x2*x4*x5*x6*x7^2*x8 + 224 -x2*x4*x5*x6*x7^2 + 225 -3*x2*x4*x5*x6*x7*x8 + 226 3*x2*x4*x5*x6*x7 + 227 2*x2*x4*x5*x6*x8 + 228 -2*x2*x4*x5*x6 + 229 -x2*x4*x5*x7^2*x8 + 230 x2*x4*x5*x7^2 + 231 2*x2*x4*x5*x7*x8 + 232 -2*x2*x4*x5*x7 + 233 -x2*x4*x5*x8 + 234 x2*x4*x5 + 235 -x2*x4*x6^2*x7*x8 + 236 x2*x4*x6^2*x7 + 237 x2*x4*x6^2*x8 + 238 -x2*x4*x6^2 + 239 -x2*x4*x6*x7^2*x8 + 240 x2*x4*x6*x7^2 + 241 2*x2*x4*x6*x7*x8 + 242 -2*x2*x4*x6*x7 + 243 -x2*x4*x6*x8 + 244 x2*x4*x6 + 245 x2*x4*x7^2*x8 + 246 -x2*x4*x7^2 + 247 -x2*x4*x7*x8 + 248 x2*x4*x7 + 249 -x2*x5^3*x6*x7*x8 + 250 x2*x5^3*x6*x7 + 251 x2*x5^3*x6*x8 + 252 -x2*x5^3*x6 + 253 x2*x5^3*x7*x8 + 254 -x2*x5^3*x7 + 255 -x2*x5^3*x8 + 256 x2*x5^3 + 257 -x2*x5*x6^2*x7*x8 + 258 x2*x5*x6^2*x7 + 259 x2*x5*x6^2*x8 + 260 -x2*x5*x6^2 + 261 -x2*x5*x6*x7^2*x8 + 262 x2*x5*x6*x7^2 + 263 3*x2*x5*x6*x7*x8 + 264 -3*x2*x5*x6*x7 + 265 -2*x2*x5*x6*x8 + 266 2*x2*x5*x6 + 267 x2*x5*x7^2*x8 + 268 -x2*x5*x7^2 + 269 -2*x2*x5*x7*x8 + 270 2*x2*x5*x7 + 271 x2*x5*x8 + 272 -x2*x5 + 273 x2*x6^2*x7*x8 + 274 -x2*x6^2*x7 + 275 -x2*x6^2*x8 + 276 x2*x6^2 + 277 x2*x6*x7^2*x8 + 278 -x2*x6*x7^2 + 279 -2*x2*x6*x7*x8 + 280 2*x2*x6*x7 + 281 x2*x6*x8 + 282 -x2*x6 + 283 -x2*x7^2*x8 + 284 x2*x7^2 + 285 x2*x7*x8 + 286 -x2*x7 + 287 x3^3*x4*x5^2*x6*x7*x8 + 288 -x3^3*x4*x5^2*x6*x7 + 289 -x3^3*x4*x5^2*x6*x8 + 290 x3^3*x4*x5^2*x6 + 291 -x3^3*x4*x5^2*x7*x8 + 292 x3^3*x4*x5^2*x7 + 293 x3^3*x4*x5^2*x8 + 294 -x3^3*x4*x5^2 + 295 -x3^3*x4*x6*x7*x8 + 296 x3^3*x4*x6*x7 + 297 x3^3*x4*x6*x8 + 298 -x3^3*x4*x6 + 299 x3^3*x4*x7*x8 + 300 -x3^3*x4*x7 + 301 -x3^3*x4*x8 + 302 x3^3*x4 + 303 -x3^3*x5^2*x6*x7*x8 + 304 x3^3*x5^2*x6*x7 + 305 x3^3*x5^2*x6*x8 + 306 -x3^3*x5^2*x6 + 307 x3^3*x5^2*x7*x8 + 308 -x3^3*x5^2*x7 + 309 -x3^3*x5^2*x8 + 310 x3^3*x5^2 + 311 x3^3*x6*x7*x8 + 312 -x3^3*x6*x7 + 313 -x3^3*x6*x8 + 314 x3^3*x6 + 315 -x3^3*x7*x8 + 316 x3^3*x7 + 317 x3^3*x8 + 318 -x3^3 + 319 x3^2*x4*x5*x6*x7^2*x8 + 320 -x3^2*x4*x5*x6*x7^2 + 321 -x3^2*x4*x5*x6*x7*x8 + 322 x3^2*x4*x5*x6*x7 + 323 -x3^2*x4*x5*x7^2*x8 + 324 x3^2*x4*x5*x7^2 + 325 x3^2*x4*x5*x7*x8 + 326 -x3^2*x4*x5*x7 + 327 -x3^2*x4*x6*x7^2*x8 + 328 x3^2*x4*x6*x7^2 + 329 x3^2*x4*x6*x7*x8 + 330 -x3^2*x4*x6*x7 + 331 x3^2*x4*x7^2*x8 + 332 -x3^2*x4*x7^2 + 333 -x3^2*x4*x7*x8 + 334 x3^2*x4*x7 + 335 -x3^2*x5*x6*x7^2*x8 + 336 x3^2*x5*x6*x7^2 + 337 x3^2*x5*x6*x7*x8 + 338 -x3^2*x5*x6*x7 + 339 x3^2*x5*x7^2*x8 + 340 -x3^2*x5*x7^2 + 341 -x3^2*x5*x7*x8 + 342 x3^2*x5*x7 + 343 x3^2*x6*x7^2*x8 + 344 -x3^2*x6*x7^2 + 345 -x3^2*x6*x7*x8 + 346 x3^2*x6*x7 + 347 -x3^2*x7^2*x8 + 348 x3^2*x7^2 + 349 x3^2*x7*x8 + 350 -x3^2*x7 + 351 x3*x4*x5^3*x6*x7*x8 + 352 -x3*x4*x5^3*x6*x7 + 353 -x3*x4*x5^3*x6*x8 + 354 x3*x4*x5^3*x6 + 355 -x3*x4*x5^3*x7*x8 + 356 x3*x4*x5^3*x7 + 357 x3*x4*x5^3*x8 + 358 -x3*x4*x5^3 + 359 -x3*x4*x5^2*x6*x7*x8 + 360 x3*x4*x5^2*x6*x7 + 361 x3*x4*x5^2*x6*x8 + 362 -x3*x4*x5^2*x6 + 363 x3*x4*x5^2*x7*x8 + 364 -x3*x4*x5^2*x7 + 365 -x3*x4*x5^2*x8 + 366 x3*x4*x5^2 + 367 x3*x4*x5*x6^2*x7*x8 + 368 -x3*x4*x5*x6^2*x7 + 369 -x3*x4*x5*x6^2*x8 + 370 x3*x4*x5*x6^2 + 371 -x3*x4*x5*x6*x7*x8 + 372 x3*x4*x5*x6*x7 + 373 x3*x4*x5*x6*x8 + 374 -x3*x4*x5*x6 + 375 -x3*x4*x6^2*x7*x8 + 376 x3*x4*x6^2*x7 + 377 x3*x4*x6^2*x8 + 378 -x3*x4*x6^2 + 379 x3*x4*x6*x7*x8 + 380 -x3*x4*x6*x7 + 381 -x3*x4*x6*x8 + 382 x3*x4*x6 + 383 -x3*x5^3*x6*x7*x8 + 384 x3*x5^3*x6*x7 + 385 x3*x5^3*x6*x8 + 386 -x3*x5^3*x6 + 387 x3*x5^3*x7*x8 + 388 -x3*x5^3*x7 + 389 -x3*x5^3*x8 + 390 x3*x5^3 + 391 x3*x5^2*x6*x7*x8 + 392 -x3*x5^2*x6*x7 + 393 -x3*x5^2*x6*x8 + 394 x3*x5^2*x6 + 395 -x3*x5^2*x7*x8 + 396 x3*x5^2*x7 + 397 x3*x5^2*x8 + 398 -x3*x5^2 + 399 -x3*x5*x6^2*x7*x8 + 400 x3*x5*x6^2*x7 + 401 x3*x5*x6^2*x8 + 402 -x3*x5*x6^2 + 403 x3*x5*x6*x7*x8 + 404 -x3*x5*x6*x7 + 405 -x3*x5*x6*x8 + 406 x3*x5*x6 + 407 x3*x6^2*x7*x8 + 408 -x3*x6^2*x7 + 409 -x3*x6^2*x8 + 410 x3*x6^2 + 411 -x3*x6*x7*x8 + 412 x3*x6*x7 + 413 x3*x6*x8 + 414 -x3*x6 + 415 -x4*x5^3*x6*x7*x8 + 416 x4*x5^3*x6*x7 + 417 x4*x5^3*x6*x8 + 418 -x4*x5^3*x6 + 419 x4*x5^3*x7*x8 + 420 -x4*x5^3*x7 + 421 -x4*x5^3*x8 + 422 x4*x5^3 + 423 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