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>
using namespace std;

long long n, t, ans = 1, c[1005];
int main()
{
    int i, j;
    cin >> n;
    for (i = 2; i <= n; i++) {
        t = i;
        for (j = 2; t > 1; j++) {
			while (t % j == 0) {
				t /= j;
				c[j]++;
			}
        }
    }
    for (i = 2; i <= n; i++) ans = ans * (c[i] + 1) % 1000000007;
    cout << ans << endl;
    return 0;
}
