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>
using namespace std;
long long a[1000], mon = 1;
int main() {
	int n; 
    cin >> n;
	for (int i = 2; i <= n; ++i) {
		int k = i;
		for (int j = 2; j <= k; ++j) {
			while (k % j == 0) {
				++a[j];
				k /= j;
			}
		}
	} 
	for (int i = 2; i <= n; ++i) {
		mon = mon * (a[i] + 1) % 1000000007;
	}
	cout << mon << endl;
}
