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 unsigned int a[1000], ans = 1;

int main() {
	int n; cin >> n;

	for (int i = 2; i <= n; i++) {
		int k = i;
		for (int j = 2; j <= k; j++) {
			while (k % j == 0) {
				a[j]++;
				k /= j;
			}
		}
	}

	for (int i = 2; i <= n; i++)ans = ans * (a[i] + 1) % 1000000007;
	cout << ans << endl;

	return 0;
}