#include <bits/stdc++.h>
using namespace std;

using LL = long long;

const LL MOD = 1000000007;
const int N = 1000000 + 5;

LL ksm(LL a, LL b) {
	LL res = 1;
	while (b) {
		if (b & 1) res = res * a % MOD;
		a = a * a % MOD;
		b >>= 1;
	}
	return res;
}

LL inv(LL x) {
	return ksm(x, MOD - 2);
}

int n, cnt, f[N], p[N], s[N];
int vis[N], hav[N], num[N];

void init() {
	s[1] = 1;
	for (int i = 2; i < N; i++) {
		if (!f[i]) p[++cnt] = i, s[i] = i;
		for (int j = 1; j <= cnt; j++) {
			if (i * p[j] >= N) break;
			f[i * p[j]] = 1;
			s[i * p[j]] = p[j];
			if (i % p[j] == 0)break;
		}
	}
}

int main(void) {
	freopen("pingfang.in", "r", stdin);
	freopen("pingfang.out", "w", stdout);
	init();
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		LL x;
		scanf("%lld", &x);
		int tot = 0;
		while (x != 1) {
			if (!vis[s[x]])
				hav[++tot] = s[x];
			vis[s[x]]++;
			x /= s[x];
		}
		for (int j = 1; j <= tot; j++) {
			if (vis[hav[j]] & 1) num[hav[j]]++;
			vis[hav[j]] = 0; 
		}
	}
	LL ans = 1;
	for (int i = 1; i <= cnt; i++) {
		if(!num[p[i]]) continue;
		ans = ans * ksm(p[i], min(num[p[i]], n - num[p[i]])) % MOD;
	}
	printf("%lld\n", ans);
	return 0;
}