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;


int main()
{
	long long N, D, K, R = 1, M = 1e9 + 7, c[1001] = {};
	cin >> N;
	while (N)
	{
		D = N;
		for (int i = 2; D != 1; i++)
		{
			while (D % i == 0)
			{
				c[i]++;
				D /= i;
			}
		}
		N--;
	}
	for (int i = 0; i < 1001; i++)
	{
		if (c[i] != 0)
		{
			R = (R * (c[i] + 1)) % M;
		}
	}
	cout << R << '\n';
}