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;

typedef long long ll;
const int MOD = 1e9 + 7;
map<int, int> mp;

int main(){
	ios::sync_with_stdio(false);
	int n;
	cin >> n;
	for(int i=2; i<=n; i++){
		//find the prime factors in N N-1 N-2....
		int x = i;
		for(int j=2; j*j<=i; j++){
			while(x%j == 0){
				mp[j]++;
				x /= j;
			}
		}
		if(x > 1)
			mp[x]++;
	}

	ll ans = 1;
	for(auto x : mp)
		ans = ans*(x.second + 1)%MOD;

	cout << ans << endl;
	return 0;
}
