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;
map<int,int> m;
void fac(int n){
  int r=n;
  for(int i=2;i*i<=n;i++){
    int exp=0;
    while(r%i==0){
      exp++;
      r/=i;
      }
      m[i]+=exp;
  }
  if(r!=1){m[r]++;}
}
int main(){
  int n;cin>>n;
  long long ans=1;
  for(int i=2;i<=n;i++){
    fac(i);
  }
  for(auto it=m.begin();it!=m.end();it++){
    ans*=(*it).second+1;
    ans=ans%1000000007;
  }
  cout<<ans;
}