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;

long long a[1000],mon=1;
int main(){
    int n;
    cin>>n;
    for(int i=2;i<=n;i++){
        int k=i;
        for(int j=2;j<=k;j++){
            while(k%j==0){
                a[j]++;
                k/=j;
            }
            
        }
    }
    for(int i=2;i<=n;i++){
        mon=mon*(a[i]+1)%1000000007;
    }
    cout<<mon<<endl;
}