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 n, i, j;
	long ans=1;
	cin >> n;
	int x, y, z,a;
	for (x = 2; x <= n; x++) {
		z = 0;
		if (x > 2) {
			for (y = 2; y < x - 1; y++) {
				if (x%y == 0)z++;
			}
		}
		if (z == 0) {
			i = 0;
			j = n;
			while (j > 1) {
				a = j % x;
				j = j - a;
				i = i + j / x;
				j = j / x;
			}
			ans = ans * (i + 1);
			if (ans >= 1000000007) ans = ans % 1000000007;
		}
	}
	cout << ans<<endl;
	return 0;
}