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 MOD = 1e9 + 7;
  int N;
  cin >> N;

  vector<int> sum(N+1, 0);
  for (int i = 2; i <= N; i++) {
    int b = i;
    for (int j = 2; j <= b; j++) {
      while (b % j == 0) {
        b /= j;
        sum[j]++;
      }
    }
  }

  long long ans = 1;
  for (int i = 0; i <= N; i++) {
    if (sum[i] > 0) ans = ans * (sum[i] + 1) % MOD;
  }

  cout << ans << endl;
}
