1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast,unroll-loops")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2,tune=native")
#pragma GCC target("sse,sse2,abm,mmx")
using namespace std;
typedef long long lld;
typedef pair<int, int> pii;
typedef pair<lld, lld> pll;
#define ff first
#define dd second
#define mp make_pair
#define pb push_back
#define sz size()
#define For(i, s, a) for(int i = s; i < a; ++i)
#define all(x) (x).begin(), (x).end()
#define make_unique(x) (x).erase(unique(all(x)), (x).end())

lld c[5001], v[5001][5001];

const lld mod = 1e9 + 7;

lld pot(lld a, lld b) {
	return !b ? 1 : (pot((a * a) % mod, b >> 1ll) * (b & 1ll ? a : 1)) % mod;
}

int main(void) {
	int n;
	scanf("%d", &n);
	For (i, 0, n)
		scanf("%lld", &c[i]);
	For (i, 0, n)
		For (j, i + 1, n) {
		lld xd = __gcd(c[i], c[j]);
		v[i][i] += xd;
		v[j][j] += xd;
		v[i][j] = v[j][i] = -xd;
	}
	const int lim = n - 1;
	For (i, 0, lim) {
		For (j, i + 1, lim) {
			if (!v[j][i])
				continue;
			lld mn = ((mod - v[j][i]) * pot(v[i][i], mod - 2)) % mod;
			For (k, i, lim)
				v[j][k] += v[i][k] * mn;
			For (k, i, lim)
				v[j][k] = v[j][k] >= mod ? v[j][k] % mod : v[j][k];
		}
	}
	lld wyn = 1;
	For (i, 0, lim)
		(wyn *= v[i][i]) %= mod;
	printf("%lld\n", (wyn + mod) % mod);
}