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;
int main() {
    int i,j,k;
    long n, s=1, M=1e9+7, a[1001]={0};
	cin>>n;
	for(i=2;i<=n;i++){
	    k=i;
	    for(j=2;k>1;){
	        if(k%j==0){
	            a[j]++;
	            k/=j;
	        }
	        else
	            j++;
	    }
	}
	for(auto x:a)
	    s = s*(x+1)%M;
	cout<<s;
}