#include<bits/stdc++.h>
using namespace std;
#define endl "\n"
#define debug(x) cout<<#x<<": "<<x<<endl
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
using ll=long long;
using ull=unsigned long long;
#define int long long
const int mo=1000000007;
vector<int> minp, primes;
 
void sieve(int n) {
    minp.assign(n + 1, 0);
    primes.clear();
    
    for (int i = 2; i <= n; i++) {
        if (minp[i] == 0) {
            minp[i] = i;
            primes.push_back(i);
        }
        
        for (auto p : primes) {
            if (i * p > n) {
                break;
            }
            minp[i * p] = p;
            if (p == minp[i]) {
                break;
            }
        }
    }
}
 
constexpr int V = 1E6;
int ksm(int a,int b,int p)
{
    int res=1;
    while(b)
    {
        if(b&1)
        {
            res=res*a%p;
        }
        a=a*a%p;
        b>>=1;
    }
    return res;
}

void solve(){
    int n;
    cin>>n;
    vector<int> a(n);
    for(int i=0;i<n;i++)
        cin>>a[i];
    ll ans=1;
    map<int,int> cnt;
    for(int i=0;i<n;i++){
        map<int,int> mp;
        int x=a[i];
        for(auto it:primes){
            if(x==1)
                break;
            while(x%it==0){
                x/=it;
                mp[it]++;
            }
        }
        int cur=1;
        for(auto [a1,a2]:mp){
            if(a2%2)
                cnt[a1]++;
        }
    }
    for(auto [a,b]:cnt){
        ans*=ksm(a,min(b,n-b),mo);
        ans%=mo;
    }
    cout<<ans;
}
signed main(){
    ios::sync_with_stdio(0);
    cout.tie(0);
    cin.tie(0);
    sieve(V);
    int t=1;
    while(t--){
        solve();
    }
}