#define _GLIBCXX_FILESYSTEM
#include<bits/stdc++.h>
using namespace std;
#define ll long long
const int mod = 1e9+7;

void solve() {
    int n;
    cin >> n;
    map<ll,ll> cnt;
    for(int i = 0; i < n; i++) {
        int x;
        cin >> x;
        for(int j = 2; j * j <= x; j++) {
            if(x % j == 0) {
                while(x % j == 0) x /= j, cnt[j]++;
            }
        }
        if(x > 1) cnt[x]++;
    }
    ll ans = 1;
    for(auto &[x,y]: cnt) {
        ans *= 1ll * (y+1);
        ans %= mod;
    }
    cout << ans << '\n';
    return;
}

int32_t main() {
    ios_base::sync_with_stdio(false);cin.tie(NULL);
    int tc = 1;
    // cin >> tc;
    for(int kase = 1; kase <= tc; kase++) {
        //cout << "Case " << kase << ": ";
        solve();
    }
    return 0;
}