You are given an integer N. Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

* 1≤N≤10^3

Input

The input is given from Standard Input in the following format:


N


Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Examples

Input

3


Output

4


Input

6


Output

30


Input

1000


Output

972926972
#include <bits/stdc++.h>
using namespace std;
int main() {
  int n;
  cin >> n;
  map<int, int> mp;

  for (int i = 2; i <= n; i++) {
    int j = 2, k = i;
    while (k > 1) {
      if (k % j == 0) {
        k /= j;
        mp[j]++;
      } else {
        j++;
      }
    }
  }
  long long ans = 1;
  for (auto c : mp) {
    ans *= (c.second + 1);
    ans %= 1000000007;
  }
  cout << ans << endl;
}
