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 long n, s=1, a[1005];
int main() {
	int i, j, k;
	cin>>n;
	for(i=2; i<=n; i++) {
		for(j=i, k=2; j>1;) {
			if(j%k==0) {
				a[k]++;
				j /= k;
			} else {
				k++;
			}
		}
	}
	for(i=2; i<=n; i++) {
		if(a[i]) s = s * (a[i]+1) % 1000000007;
	}
	cout << s;
	return 0;
}