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>
using namespace std;
long long n, s=1, M=1e9+7, a[1005];
int main() {
	int i, j, k;
	cin>>n;
	for(j=1; j<=n; j++) {
		k = j;
		for(i=2; k>1; ) {
			if(k%i==0) k/=i, a[i]++;
			else i++;
		}
	}
	for(i=2; i<=n; i++) s = s*(a[i]+1)%M;
	cout<<s;
	return 0;
}