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 = 2; i <= N; i++) {
    int s = i;
    for (int j = 2; j <= i; j++) {
      while (s%j == 0) {
        x.at(j-1)++;
        s /= j;
      }
    }
  }
  long ans = 1;
  for (int i = 0; i < N; i++) {
    ans *= x.at(i);
    ans %= 1000000007;
  }
  cout << ans << endl;
}