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 N;
long mod = 1e9 + 7;
long sum = 1;
long a[1001];
int main() {
	cin >> N;
	for (int i = 2; i <= N; ++i) {
		int k = i;
		for (int j = 2; k > 1;) {
			if (k%j == 0) {
				a[j]++;
				k /= j;
			}
			else {
				j++;
			}
		}
	}
	for (int i = 2; i <= N; ++i) {
		sum *= (a[i] + 1);
		sum %= mod;
	}
	cout << sum << endl;
	return 0;
}