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