QUIZZ

#include <bits/stdc++.h>
#define ll long long
#define ld long double
#define ull unsigned long long
#define pb push_back
#define pii pair<int, int>
#define pll pair<ll, int>
#define pld pair<ld, ll>
#define fi first
#define se second
using namespace std;
const int N = 2e5+5;
const int M = 1e4+5;
const ll mod = 1e9+7;
const ll inf = 1e15;
const ld base = 1e-6;
int n, t, m, k, a[N], ans, lab[N], d[N], tong, l[N], r[N];
vector<pii> adj[N];
vector<int> vi;
ll pw(ll k, ll n)
{

    ll total = 1;
    for(; n; n >>= 1)
    {
        if(n&1)total = total * k % mod;
        k = k * k % mod;
    }
    return total;
}
void sol()
{
    cin >> n;
    for(int i = 2; i < N; i ++)
    {
        if(!d[i])
            for(int j = i; j < N; j += i)d[j] = i;
    }
    for(int i = 1; i <= n; i ++)
    {
        cin >> a[i];
        while(a[i] > 1)
        {
            k = d[a[i]];
            m = 1;
            while(a[i] % k ==0)
            {
                m *= k;
                a[i] /= k;
            }
            adj[k].pb({i, m});
        }
    }
    ans = 1;
    for(int i = 2; i < N; i ++)
    {
        if(adj[i].empty())continue;
        vi.clear();
        m = adj[i].size();
        for(int j = 0; j < m; j ++)
        {
            while(!vi.empty() && adj[i][vi.back()].se <= adj[i][j].se)vi.pop_back();
            l[j] = vi.empty() ? 0 : adj[i][vi.back()].fi;
            vi.pb(j);
        }
        vi.clear();
        for(int j = m-1; j >= 0; j --)
        {
            while(!vi.empty() && adj[i][vi.back()].se < adj[i][j].se)vi.pop_back();
            r[j] = vi.empty() ? n+1 : adj[i][vi.back()].fi;
            ans = 1ll * pw(adj[i][j].se % mod, 1ll*(adj[i][j].fi-l[j]) * (r[j]-adj[i][j].fi) ) * ans % mod;
            vi.pb(j);
        }
    }
    cout << ans;
}
int main()
{
    cin.tie(0);
    cout.tie(0);
    ios_base::sync_with_stdio(0);
    #define task "QUIZZ"
    if(fopen(task".inp", "r"))
    {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    int test = 1;
    //cin >> test;
    while(test -- > 0)sol();
    return 0;
}