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;
using ll=long long;

const int MOD=1000000000+7;

int main(){
  int n;
  cin >> n;
  ll ans=1;
  map<int,int> mp;
  for(int i=n;i>1;--i){
    int j=i;
    int k=2;
    while(j>1){
      if(j%k==0){
        mp[k]++;
        j=j/k;
      }else{
        k++;
      }
    }
  }
  for(auto p : mp){
    ans=ans*(p.second+1)%MOD;
    ans=ans%MOD;
  }
  cout << ans << endl;
}
