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()
{
    long long n, i, ans=1, cnt[1001]={0}, tmp, j;

    cin >> n;
    
    for(i=2;i<=n;i++){
        tmp=i;
        for(j=2;j<=i;j++){
            while(tmp%j==0){
                cnt[j]++;
                tmp=tmp/j;
            }
        }
    }
    for(i=2;i<=n;i++){
        ans=ans*(cnt[i]+1);
        ans=ans%1000000007;
    }
    
    cout << ans <<endl;
    return 0;
}