#include <bits/stdc++.h>
using namespace std;
const int N = 1e5, mod = 1e9 + 7;
int su[N], f;
int cnt[N];
int view[N];
int a[N];
int dp[510][15100];
long long ans = 1;
int main() {
  for (int i = 2; i < N; ++i) {
    if (!view[i]) su[f++] = i;
    for (int j = 2; j * i < N; ++j) {
      view[i * j] = 1;
      if (i % j == 0) break;
    }
  }
  for (int i = 0; i < 510; ++i) dp[i][0] = 1;
  for (int i = 1; i < 15100; ++i) {
    dp[1][i] = 1;
  }
  for (int i = 2; i < 510; ++i) {
    for (int j = 1; j < 15100; ++j) {
      dp[i][j] = dp[i][j - 1] + dp[i - 1][j];
      if (dp[i][j] >= mod) dp[i][j] -= mod;
    }
  }
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; ++i) {
    int tmp;
    scanf("%d", &tmp);
    for (int j = 0; j < f; ++j) {
      while (tmp % su[j] == 0) {
        cnt[j]++;
        tmp /= su[j];
      }
    }
    if (tmp != 1) {
      su[f++] = tmp;
      cnt[f - 1]++;
    }
  }
  for (int i = 0; i < f; ++i) {
    ans = ans * dp[n][cnt[i]] % mod;
  }
  printf("%d\n", (int)ans);
  return 0;
}
