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 INF 10000001

#define MOD 1000000007

typedef long long ll;

int main(void){
  int n,i,j;
  std::cin >> n;
  std::map<int,int> mp;
  for(i=2;i<=n;i++){
    int x = i;
    for(j=2;j<=x;j++){
      while(x%j==0){
        x /= j;
        mp[j]++;
      }
    }
  }
  ll ans = 1;
  for(auto &t:mp){
    ans = ((ans%MOD)*(t.second+1)%MOD)%MOD;
  }
  std::cout << ans << std::endl;
  return 0;
}
