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 <stdio.h>
#include <string.h>
#define MOD 1000000007

int N;
long long int ps[1123];
long long int ans = 1;

void d(int v) {
	int a = v, i, j, res = 1;
	for (j = 2; j <= v; ++j)
	{
		for (i = 0; a % j == 0; ++i) { a /= j; }
		ps[j - 1] += i;
	}
}

int main(void)
{
	scanf("%d", &N);

	for (int i = N; i >= 2; --i)
	{
		d(i);
	}
	for (int i = 0; i < N; ++i)
	{
		ans *= ps[i] + 1;
		ans %= MOD;
	}

	printf("%lld\n", ans);
	return 0;
}