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;

long long ans = 1;
int n;
map<int, int> f;

void factorization(int n){
	for(int i = 2; i <= n; ++i){
		while(n % i == 0){
			f[i]++;
			n /= i;
		}
	}
}

int main(){
	cin >> n;
	
	for(int i = 1; i <= n; ++i) factorization(i);
	for(auto itr = f.begin(); itr != f.end(); itr++){
		ans *= (itr->second+1);
		ans %= 1000000007;
	}
	cout << ans << endl;
}