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(){
	int n; cin >> n;
	map<int,int> p;
	for(int i = 2; i <= n; i++){
		int k = i;
		for(int j = 2; j*j <= k; j++){
			if(k % j == 0){
				int c = 0;
				while(k % j == 0) k /= j, c++;
				p[j] += c;
			}
		}
		if(k != 1) p[k] += 1;
	}
	int ans = 1;
	for(auto e : p) ans = 1ll * ans * (e.second + 1) % 1000000007;
	cout << ans << endl;
	return 0;
}
