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 <vector>
using namespace std;

const long long int DENOMI = 1000000007;

int main()
{
	int n;
	cin >> n;
	auto f = vector<int>(n + 1);
	for(auto i = 2; i <= n; ++i){
		int t = i;
		for(auto j = 2; j <= t; ++j){
			while(t % j == 0){
				++f[j];
				t /= j;
			}
		}
	}
	long long int ans = 1;
	for(auto i = 2; i <= n; ++i){
		ans = (ans * (f[i] + 1)) % DENOMI;
	}
	cout << ans << endl;
	return 0;
}