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>

int counts[1001];

int main(int argc, char *argv[]){
	int n;
	std::cin >> n;

	for(int i = 2;i <= n; i++){
		int x = i;
		for(int j = 2; x > 1;){
			if(x % j == 0){
				counts[j]++;
				x /= j;
			}else{
				j++;
			}
		}
	}
	unsigned long long result = 1;
	for(int i = 2; i <= 1000; i++){
		if(i > 0)
			result = (result * (counts[i] + 1)) % 1000000007;
	}
	std::cout << result << std::endl;
	return 0;
}
