mirror of
https://github.com/Kiritow/OJ-Problems-Source.git
synced 2024-03-22 13:11:29 +08:00
104 lines
2.4 KiB
C++
104 lines
2.4 KiB
C++
#include <iostream>
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#include <cstdio>
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#include <cmath>
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#include <vector>
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#include <cstring>
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#include <algorithm>
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#include <string>
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#include <set>
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#include <ctime>
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#include <queue>
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#include <map>
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#include <sstream>
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#define CL(arr, val) memset(arr, val, sizeof(arr))
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#define REP(i, n) for((i) = 0; (i) < (n); ++(i))
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#define FOR(i, l, h) for((i) = (l); (i) <= (h); ++(i))
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#define FORD(i, h, l) for((i) = (h); (i) >= (l); --(i))
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#define L(x) (x) << 1
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#define R(x) (x) << 1 | 1
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#define MID(l, r) (l + r) >> 1
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#define Min(x, y) x < y ? x : y
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#define Max(x, y) x < y ? y : x
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#define E(x) (1 << (x))
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const double eps = 1e-4;
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typedef long long LL;
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const int inf = ~0u>>2;
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using namespace std;
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const int N = 110;
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const int M = 1000010;
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const int MOD = 1e9 + 7;
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int c[N][N];
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int k[M], t[M];
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int num, n;
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int prime[N*20];
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bool vis[N*20];
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int cnt;
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void get_prime() {
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CL(vis, true);
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int i, j;
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for(i = 2; i < N*20; ++i) {
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for(j = i*i; j < N*20; j += i) {
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vis[j] = false;
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}
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}
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cnt = 0;
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for(i = 2; i < N*20; ++i) {
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if(vis[i]) prime[cnt++] = i;
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}
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}
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void init() {
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get_prime();
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CL(c, 0);
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int i , j;
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for(i = 0; i < N; ++i) c[i][0] = c[i][i] = 1;
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for(i = 2; i < N; ++i) {
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for(j = 1; j < i; ++j) {
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c[i][j] = (c[i-1][j] + c[i-1][j-1])%MOD;
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}
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}
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}
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LL solve(int x) {
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int m = n, flag = 1, i;
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for(i = 0; i < n; ++i) {
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if(((1<<i)&x) == 0) {
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flag *= -1; m--;
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}
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}
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LL tmp = 1;
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for(i = 0; i < num; ++i) {
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tmp = tmp*LL(c[k[i]+m-1][m-1])%MOD;
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}
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return tmp*flag;
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}
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int main() {
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init();
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int x, i, j;
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LL ans;
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while(~scanf("%d", &n)) {
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CL(t, 0);
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for(i = 0; i < n; ++i) {
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scanf("%d", &x);
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for(j = 0; prime[j]*prime[j] <= x; ++j) {
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if(x%prime[j] == 0) {
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while(x%prime[j] == 0) {
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t[prime[j]]++; x /= prime[j];
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}
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}
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}
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if(x != 1) t[x]++;
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}
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num = 0;
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for(i = 2; i < M; ++i) {
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if(t[i] != 0) {
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k[num++] = t[i];
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}
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}
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ans = 0;
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for(i = (1<<n)-1; i >= 1; --i) {
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ans = (ans + solve(i))%MOD;
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}
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cout << (ans%MOD + MOD)%MOD << endl;
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}
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return 0;
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}
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