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;

const int INF = 1e9+7;

int main() {
	int n;
	cin >> n;
	vector<int> x(n+1);
	for(int i=0; i<n+1; i++){
		x.at(i) = 0;
	}
	for(int i=2; i<n+1; i++){
		int num = i;
		for(int j=2; j<=n; j++){
			while(num%j == 0){
				x.at(j)++;
				num /= j;
			}
		}
	}
	long long ans = 1;
	for(int i=2; i<=n; i++){
		ans *= x.at(i)+1;
		ans %= INF;
	}
	cout << ans << endl;

}