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;

typedef long long ll;

const int MAX_N = 1010;
const ll P = 1000000007;

int a[MAX_N];

int main() {
	int N;
	cin >> N;
	for (int i = 2; i <= N; i++) {
		int t = i;
		for (int d = 2; d <= t; d++) {
			while (t % d == 0) {
				a[d] += 1;
				t /= d;
			}
		}
		if (t != 1) a[t] += 1;
	}
	ll ans = 1;
	for (int p = 2; p <= N; p++) {
		if (a[p] != 0) ans = (ans * (a[p] + 1)) % P;
	}
	cout << ans << endl;
	return 0;
}

