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;
 
bool isPrime (int x) {
    for(int i=2; i*i <=x; i++) {
        if(x%i==0) return false;
    }
    return true;
}
 
int N;
int main () {
    cin >> N;
    long long int ans = 1;
    for(int i=2; i<=N; i++) {
        if(isPrime(i)) {
            long long int r = 1;
            for(int x=N; x/=i; r+=x);
            ans = ans * r % 1000000007;
        }
    }
    cout << ans << endl;
    return 0;
}