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<bits/stdc++.h>
using namespace std;

const int M = 1e9+7;

int main(){
	int n;
	cin>>n;

	vector<int> arr(1001);

	for(int i=2;i<=n;i++){
		if(arr[i]==0){
			for(int j=i+i;j<=n;j+=i) arr[j] = 1;
		}
	}

	int res = 1;
	for(int i=2;i<=n;i++){
		if(arr[i]==0){
			int t = 0;
			for(int j=i;j<=n;j*=i) t+=n/j;
				res = 1ll*res*(t+1)%M;
		}
	}
	cout<<res;
}