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 <cstdio>
typedef long long LL;

const int mod = 1e9 + 7;
LL p[1010];

void getp(int x) {
	for(int i = 2; i * i <= x; ++i) {
		if(x % i == 0) {
			while(x % i == 0) {
				p[i]++;
				x /= i;
			}
		}
	}
	if(x > 1) p[x]++;
}

int main() {
	int n;
	scanf("%d", &n);
	for(int i = 2; i <= n; ++i) {
		getp(i);
	}
	LL sum = 1;
	for(int i = 1; i <= n; ++i) {
		sum = (sum * (p[i] + 1)) % mod;
	}
	printf("%lld\n", sum);
	return 0;
}