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 <vector>
using namespace std;
typedef long long int lli;
const lli mod = 1e9 +7;

int main(){
	lli n;
	cin >> n;
	vector<lli> pri(1000, 1);
	for(int i=2; i<=n; i++){
		int num=i;
		for(int j=2; j*j<=n; j++){
			while(num%j==0){
				pri[j]++;
				num /= j;
			}
		}
		pri[num]++;
	}
	lli ans=1;
	for(int i=2; i<1000; i++){
		ans = ans*pri[i] %mod;
	}
	cout << ans << endl;
	return 0;
}