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 <cstdio>

#define MOD 1000000007
using namespace std;

int main(void){
    int n;
    long long c[10005], ans=1, t;
    cin >> n;

    for(int i=2; i<=n; i++){
        t = i;
        for(int j=2; t > 1;j++){
            while(t%j == 0){
                t = t / j;
                c[j]++;
            }
        }
    }

    for(int i=2; i<=n; i++){
        ans = ans * (c[i] + 1) % MOD;
    }

    cout << ans <<endl;
    
    return 0;
}