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;

int counter[1005];

void setcount(int n){
  int i=2;
  while(n>=i){
    if(n%i==0) {
      counter[i]++;
      n/=i;
    }else i++;
  }
}

int main(){
  int N;
  long long sum=1;
  long long figure=pow(10,9)+7;
  cin >> N;
  for(int i=0;i<=N;i++) counter[i]=0;

  for(int i=2;i<=N;i++) setcount(i);
  for(int i=1;i<=N;i++){
    sum *=(counter[i]+1);
    if(sum>figure) sum%=figure;
  }
  cout << sum << endl;;
  return 0;
}
