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<bits/stdc++.h>
using namespace std;
int main()
{
  const int mod = 1e9 + 7;
  int n;
  cin >> n;
  long long ans = 1;
  vector<int> p(n + 1);
  for (int i = 2; i <= n; i++) {
	int s = i;
	int t = 2;
	while (s >= t * t) {
	  if (s % t == 0) {
		p[t]++;
		s /= t;
	  }
	  else {
		t++;
	  }
	}
	p[s]++;
  }
  for (int i = 2; i <= n; i++) {
	ans = ans * (p[i] + 1) % mod;
  }
  cout << ans << endl;

  return 0;
}

