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 <unordered_map>
#include <utility>
using namespace std;

int main() {
	int N;
	cin >> N;
	unordered_map<int, long> a;
	for (int i = 1; i <= N; i++) {
		int b = i;
		for (int j = 2; j * j <= b; j++) {
			while (b % j == 0) {
				a[j]++;
				b /= j;
			}
		}
		if (b != 1) a[b]++;
	}
	long ans = 1;
	for (pair<const int, long>& i : a) {
		ans *= i.second + 1;
		ans %= 1000000007;
	}
	cout << ans;
}