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>
#include <algorithm>
#include <string>
using namespace std;
long long a[1005];
int main(void){
	int n; cin>>n;
    for(int i=1;i<=n;i++){
        int k=i;
        for(int j=2;j*j<=k;j++){
            while(k%j==0){
                a[j]++;
                k/=j;
            }
        }
        if(k!=1){
            a[k]++;
        }
    }
    long long ans=1;
    for(int i=0;i<1005;i++){
		ans=ans*(a[i]+1)%1000000007;
	}
	cout<<ans<<endl;
    
}
