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 <iostream>

int N;
int sum[1005];
int main(){
  std::cin>>N;
  
  int temp=0;
  for(int i=2;i<=N;++i){
    temp = i;
    for(int j=2;j<=N;++j){
      if(temp==0)
        break;
      while(temp%j==0){
        temp/=j;
        ++sum[j];
      }
    }
  }
  
  long long ans =1;
  for(int i=2;i<=N;++i)
    ans=ans*(sum[i]+1)%1000000007;
  
  std::cout<<ans<<std::endl;
}