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>
#include <cstdio>
#include <cmath>
#define N 1000000007
#define M 1000
using namespace std;

int main() {
	long long n,ans=1;
	long long yaku[M]={0};
	cin>>n;
	
	for(int i=1;i<=n;i++){
		int a=i;
		int cnt=2;
		while(a!=1){
			if(a%cnt==0){
				a=a/cnt;
				yaku[cnt]++;
			}else{
				cnt++;
			}
		}
	}
	
	for(int i=0;i<M;i++){
		ans=(ans*(yaku[i]+1))%N;
	}
	cout<<ans<<endl;
	return 0;
}