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>
#define ll long long
using namespace std;

const ll mod = 1e9+7;

int main() {
  int n;
  cin >> n;

  vector<int> a(n+1);
  for (int i = 2; i <= n; i++) {
    int tmp = i;
    for (int j = 2; j <= tmp; j++) {
      while (tmp > 0 && tmp % j == 0) {
        a[j]++;
        tmp/=j;
      }
    }
  }
  ll ans = 1;
  for (int i = 0; i <= n; i++) {
    if (a[i] != 0) {
      ans *= (a[i] + 1);
      ans %= mod;
    }
  }
  cout << ans << endl;
}
