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;
const long long MOD=1000000007;

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