简要题意：
亲爱的张老师喜欢van全平方数。
现在他手中有n个整数，分别为a1,a2,...,an。
他想知道：在这个数组的 2n-1 个非空子数组中，有多少满足所有数的乘积是完全平方数。
数据范围：1<=n<=500; 1<=ai<=109
分析：
当看到1<=ai<=109时，这道题很显然必须得分解质因数！
每个ai被分为pj的kj次方。
想到完全平方数的每个质因数的指数必为偶数，我们可以把这道题转化为异或方程！
共n个未知数xi，若xi==1，表示选ai；否则不选ai。
有m个方程，表示m种质因数，第i个方程中，A[i][n+1]=0，这样可以保证每个质因数的指数为偶数！
若ai包含某个质因数k，且指数为奇数，则A[k][i]=1，表示选择ai会给质因数k贡献1。
转化完成后，只需要套高斯消元的模板，算有cnt个*变元，答案就是2cnt-1。
值得注意的是，1<=n<=500，换句话说，cnt可能有500之大，我们必须用高精！
当然，这个高精还是挺好写的，注意点细节就行了。
#include<bits/stdc++.h>
using namespace std;
#define re register int
bitset<2000>A[5000];
int cnt[500];int len,B[500];
inline void modi()
{
for(re i=1;i<=len;++i)
{
cnt[i]=cnt[i]<<1;
cnt[i]+=B[i];B[i]=0;
while(cnt[i]>9)cnt[i]-=10,B[i+1]++;
}
while(cnt[len+1]||B[len+1])len++,cnt[len]+=B[len],B[len]=0;
}
inline void prin()
{
int tmp=1;cnt[tmp]--;
while(cnt[tmp]<0)cnt[tmp]+=10,cnt[++tmp]--;
while(cnt[len]==0&&len>1)len--;
for(re i=len;i;--i)printf("%d",cnt[i]);
}
void Gauss(const int n, const int m){
for(re x=1,y=1;x<=n&&y<m;++x,++y){
int mx=x;for(re i=x+1;i<=n&&A[mx][y]==0;++i)mx=i;
if(A[mx][y]==0){--x;modi();continue;}
if(mx!=x)swap(A[mx],A[x]);
for(re i=x+1;i<=n;++i) if(A[i][y]) A[i]^=A[x];
}prin();
return;
}
int pri[3500]={0,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,16411,16417,1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09,24733,24749,24763,24767,24781,24793,24799,24809,24821,24841,24847,24851,24859,24877,24889,24907,24917,24919,24923,24943,24953,24967,24971,24977,24979,24989,25013,25031,25033,25037,25057,25073,25087,25097,25111,25117,25121,25127,25147,25153,25163,25169,25171,25183,25189,25219,25229,25237,25243,25247,25253,25261,25301,25303,25307,25309,25321,25339,25343,25349,25357,25367,25373,25391,25409,25411,25423,25439,25447,25453,25457,25463,25469,25471,25523,25537,25541,25561,25577,25579,25583,25589,25601,25603,25609,25621,25633,25639,25643,25657,25667,25673,25679,25693,25703,25717,25733,25741,25747,25759,25763,25771,25793,25799,25801,25819,25841,25847,25849,25867,25873,25889,25903,25913,25919,25931,25933,25939,25943,25951,25969,25981,25997,25999,26003,26017,26021,26029,26041,26053,26083,26099,26107,26111,26113,26119,26141,26153,26161,26171,26177,26183,26189,26203,26209,26227,26237,26249,26251,26261,26263,26267,26293,26297,26309,26317,26321,26339,26347,26357,26371,26387,26393,26399,26407,26417,26423,26431,26437,26449,26459,26479,26489,26497,26501,26513,26539,26557,26561,26573,26591,26597,26627,26633,26641,26647,26669,26681,26683,26687,26693,26699,26701,26711,26713,26717,26723,26729,26731,26737,26759,26777,26783,26801,26813,26821,26833,26839,26849,26861,26863,26879,26881,26891,26893,26903,26921,26927,26947,26951,26953,26959,26981,26987,26993,27011,27017,27031,27043,27059,27061,27067,27073,27077,27091,27103,27107,27109,27127,27143,27179,27191,27197,27211,27239,27241,27253,27259,27271,27277,27281,27283,27299,27329,27337,27361,27367,27397,27407,27409,27427,27431,27437,27449,27457,27479,27481,27487,27509,27527,27529,27539,27541,27551,27581,27583,27611,27617,27631,27647,27653,27673,27689,27691,27697,27701,27733,27737,27739,27743,27749,27751,27763,27767,27773,27779,27791,27793,27799,27803,27809,27817,27823,27827,27847,27851,27883,27893,27901,27917,27919,27941,27943,27947,27953,27961,27967,27983,27997,28001,28019,28027,28031,28051,28057,28069,28081,28087,28097,28099,28109,28111,28123,28151,28163,28181,28183,28201,28211,28219,28229,28277,28279,28283,28289,28297,28307,28309,28319,28349,28351,28387,28393,28403,28409,28411,28429,28433,28439,28447,28463,28477,28493,28499,28513,28517,28537,28541,28547,28549,28559,28571,28573,28579,28591,28597,28603,28607,28619,28621,28627,28631,28643,28649,28657,28661,28663,28669,28687,28697,28703,28711,28723,28729,28751,28753,28759,28771,28789,28793,28807,28813,28817,28837,28843,28859,28867,28871,28879,28901,28909,28921,28927,28933,28949,28961,28979,29009,29017,29021,29023,29027,29033,29059,29063,29077,29101,29123,29129,29131,29137,29147,29153,29167,29173,29179,29191,29201,29207,29209,29221,29231,29243,29251,29269,29287,29297,29303,29311,29327,29333,29339,29347,29363,29383,29387,29389,29399,29401,29411,29423,29429,29437,29443,29453,29473,29483,29501,29527,29531,29537,29567,29569,29573,29581,29587,29599,29611,29629,29633,29641,29663,29669,29671,29683,29717,29723,29741,29753,29759,29761,29789,29803,29819,29833,29837,29851,29863,29867,29873,29879,29881,29917,29921,29927,29947,29959,29983,29989,30011,30013,30029,30047,30059,30071,30089,30091,30097,30103,30109,30113,30119,30133,30137,30139,30161,30169,30181,30187,30197,30203,30211,30223,30241,30253,30259,30269,30271,30293,30307,30313,30319,30323,30341,30347,30367,30389,30391,30403,30427,30431,30449,30467,30469,30491,30493,30497,30509,30517,30529,30539,30553,30557,30559,30577,30593,30631,30637,30643,30649,30661,30671,30677,30689,30697,30703,30707,30713,30727,30757,30763,30773,30781,30803,30809,30817,30829,30839,30841,30851,30853,30859,30869,30871,30881,30893,30911,30931,30937,30941,30949,30971,30977,30983,31013,31019,31033,31039,31051,31063,31069,31079,31081,31091,31121,31123,31139,31147,31151,31153,31159,31177,31181,31183,31189,31193,31219,31223,31231,31237,31247,31249,31253,31259,31267,31271,31277,31307,31319,31321,31327,31333,31337,31357,31379,31387,31391,31393,31397,31469,31477,31481,31489,31511,31513,31517,31531,31541,31543,31547,31567,31573,31583,31601,31607,31627,31643,31649,31657,31663,31667,31687,31699,31721,31723,31727,31729,31741,31751,31769,31771,31793,31799,31817,31847,31849,31859,31873,31883,31891,31907,31957,31963,31973,31981,31991};
map<int,int>mp;
signed main()
{
cnt[1]=1;len=1;
int n, Tot=0; scanf("%d",&n);
for(re i=1;i<=n;++i)
{
int x;scanf("%d",&x);
for(re j=1;j<=3432 && pri[j]<=x && x>1;++j)
{
if(x%pri[j]==0)
{
int tmp=0;
while(x%pri[j]==0){tmp^=1;x/=pri[j];}
if(tmp)
{
if(!mp.count(pri[j]))
{
mp[pri[j]]=++Tot;
A[Tot][n+1]=0;
}
A[mp[pri[j]]][i]=1;
}
}
}
if(x>1)
{
if(!mp.count(x))
{
mp[x]=++Tot;
A[Tot][n+1]=0;
}
A[mp[x]][i]=1;
}
}Gauss(Tot+10,n+1);
return 0;
}
“考场莫嫌高精烦，后知后觉悔莫及”----《kzsn语录》kzsn