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>
#include<string>
#include<algorithm>
#include<bits/stdc++.h>
using namespace std;

int main(){ 
int N,sum[2000];
  cin >> N;
  
  int a=0;
  for(int i=2;i<=N;i++){
    a = i;
    for(int j=2;j<=N;j++){
      if(a==0){
        break;
      }
      while(a%j==0){
        a/=j;
        sum[j] += 1;
      }
    }
  }
  
  long long b=1;
  for(int i=2;i<=N;i++){
    b=b*(sum[i]+1)%1000000007;
  }
    cout << b << endl;
    return 0;
}