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 <map>

using namespace std;

typedef long long ll;

const ll MOD = 1000000007;

map<int, int> p;

void prime(int n) {
	for (int i = 2; i*i <= n; i++) {
		while (n%i == 0) {
			++p[i];
			n /= i;
		}
	}
	if (n != 1)p[n]++;
}

int main() {
	int n;
	cin >> n;
	for (int i = 2; i <= n; i++) {
		prime(i);
	}
	ll ans = 1;
	for (int i = 2; i <= n; i++) {
		ans *= 1 + p[i];
		ans %= MOD;
	}
	cout << ans << endl;
	return 0;
}