#include <bits/stdc++.h>
using namespace std;
const int mod = 1000000007;
int n;
int a[100100];
long long c[17010][600];
int main() {
  scanf("%d", &n);
  map<int, int> q;
  c[0][0] = 1;
  for (int i = 1; i <= 16666; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= 502; j++) {
      c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % mod;
    }
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    int m = a[i];
    for (int i = 2; i * i <= m; i++) {
      if (m % i == 0) {
        while (m % i == 0) {
          q[i]++;
          m /= i;
        }
      }
    }
    if (m > 1) {
      q[m]++;
    }
  }
  long long ans = 1;
  map<int, int>::iterator it;
  for (it = q.begin(); it != q.end(); it++) {
    int xx = it->second;
    ans *= c[xx + n - 1][n - 1];
    ans %= mod;
  }
  printf("%lld\n", ans);
  return 0;
}
