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<string>
#include<algorithm>

using namespace std;

int main() {
	int MOD = 1000000007;
	int factor[1001] = {};
	long long n, ans = 1;
	cin >> n;
	for (int i = 2; i <= n; i++) {
		int divide = 2;
		int num = i;
		while (num != 1) {
			if (!(num % divide))factor[divide]++,num /= divide;
			else divide++;
		}
	}
	for (int i = 2; i <= n; i++) {
		ans = ans * (factor[i] + 1);
		ans %= MOD;
	}
	cout << ans << endl;
	return 0;
}