#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <vector>
#include <queue>
#include <cmath>
#include <stack>
#include <map>
#include <set>
#include <deque>
#include <cstring>
#include <functional>
#include <climits>
#include <list>
#include <ctime>
#include <complex>
 
#define F1(x,y,z) for(int x=y;x<z;x++)
#define F2(x,y,z) for(int x=y;x<=z;x++)
#define F3(x,y,z) for(int x=y;x>z;x--)
#define F4(x,y,z) for(int x=y;x>=z;x--)
#define pb push_back
#define LL long long
#define co complex<double>
 
#define MAX 100005
#define AMAX 1500
#define MOD 1000000007

#define f(c,d) ((1<<(c))*(d))

using namespace std;

int n,ta,tt;
LL tb,tc;
map<int,LL> x;
map<int,LL>::iterator it;
vector<int> prime;
vector<LL> pro;
bool ok;

LL po(LL b,LL p){
    if(!p)return 1;
    if(p&1)return b*po(b,p-1)%MOD;
    LL t=po(b,p>>1);
    return t*t%MOD;
}

int main(){
    F1(a,2,MAX){
        if(a*a>MAX)break;
        ok=1;
        F1(b,0,prime.size()){
            if(prime[b]*prime[b]>a)break;
            if(a%prime[b]==0){
                ok=0;
                break;
            }
        }
        if(ok)prime.pb(a);
    }
    while(scanf("%d",&n)==1){
        x.clear();
        scanf("%d",&ta);
        F2(a,2,n){
            tt=a;
            scanf("%d",&ta);
            F1(b,0,prime.size()){
                if(prime[b]*prime[b]>tt)break;
                if(tt%prime[b]==0){
                    it=x.insert(make_pair(prime[b],0LL)).first;
                    while(tt%prime[b]==0){
                        tt/=prime[b];
                        it->second+=ta;
                    }
                }
            }
            if(tt!=1)x[tt]+=ta;
        }
        ok=1;
        pro.clear();
        pro.pb(1LL);
        for(it=x.begin();it!=x.end();++it){
            tb=it->second+1;
            if(tb%2==0&&ok){
                tb/=2;
                ok=0;
            }
            pro.back()=pro.back()*tb%(MOD-1);
        }
        tb=1;
        for(it=x.begin();it!=x.end();++it){
            if(ok)tc=po(it->first,it->second/2);
            else tc=po(it->first,it->second);
            F1(a,0,pro.size())tc=po(tc,pro[a]);
            tb=tb*tc%MOD;
        }
        printf("%I64d\n",tb);
    }
    //system("pause");
    return 0;
}