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;

long long n, ans=1, a[1005];
void f(int p) {
    int i;
    for(i=2; p>1; ) {
        if(p % i == 0) {
            a[i]++;
            p /= i;
        } else {
            i++;
        }
    }
}

int main()
{
    int i;
    cin >> n;
    for(i=2; i<=n; i++) {
        f(i);
    }
    for(i=2; i<=n; i++) {
        ans = ans * (a[i]+1) % 1000000007;
    }
    cout << ans;
    return 0;
}
