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>
using namespace std;
int main(void){
    int n;
    cin>>n;
    int a[1001] = {0};
    for(int i=0;i<=n;i++){
        int b=i,j=2;
        while(b>1){
            if(b%j==0){
                b=b/j;
                a[j]++;
            }else{
                j++;
            }
        }
    }
    long long c=1,p=1000000007;
    for(int i=1;i<=n;i++){
        c*=a[i]+1;
        c=c%p;
    }
    cout<<c<<endl;
    
}
