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;
  vector<int> x(n, 1);
  for (int i = 1; i <= n; i++) {
    int m = i;
    for (int j = 2; j * j <= m; j++) {
      while (m % j == 0) {
        m /= j;
        x.at(j - 1)++;
      }
    }
    if (m > 1) x.at(m - 1)++;
  }
  long ans = 1;
  const long mod = 1000000007;
  for (int i = 0; i < n; i++) {
    ans *= x.at(i);
    ans %= mod;
  }
  cout << ans << endl;
}
