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 N;
long long P[1001];

void factorize(int n){
	while(!(n % 2))
		P[2]++, n /= 2;
	for(int i = 3; i <= sqrt(n); i += 2)
		while(!(n % i))
			P[i]++, n /= i;
	if(n > 2) P[n]++;
}

int main(){
	scanf("%d", &N);
	for(int i = 2; i <= N; i++) factorize(i);
	long long res = 1;
	for(int i = 1; i < 1001; i++)
		if(P[i] > 0){
			res *= (P[i] + 1);
			res %= 1000000007;
		}
	printf("%d\n", res);
	return 0;
}
