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<string>
#include<vector>
#include<algorithm>
using namespace std;
long long a[2000], n, cnt, mod = 1000000007;
int main() {
	cin >> n; cnt = 1;
	for (int i = 1; i <= n; i++) {
		int p = i;
		for (int j = 2; j <= n; j++) {
			while (p%j == 0) { p /= j; a[j]++; }
		}
	}
	for (int i = 1; i <= n; i++) { cnt *= (a[i] + 1); cnt %= mod; }
	cout << cnt << endl;
	return 0;
}
