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 <bits/stdc++.h>
using namespace std;

int main() {
	ios_base::sync_with_stdio( false );

	int N;
	cin >> N;

	map<int, int> p;
	for( int i = 1; i <= N; ++i ) {
		int x = i;
		int y = 2;

		while( x > 1 ) {
			if( x % y ) {
				y += 1;
			}
			else {
				p[y] += 1;
				x /= y;
			}
		}
	}

	int64_t result = 1;
	int64_t m = 1000000007;

	for( auto& v: p ) {
		result = result * (v.second + 1) % m;
	}

	cout << result << endl;
}
