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()
{
  int n;
  cin >> n;
  vector<int> a(n+1);
  for(int i = 2; i <= n;i++) {
   	int tmp = i;
    while(tmp % 2 == 0) {
    	tmp /= 2;
      	a[2]++;
    }
    for(int j = 3; j <= tmp;j+=2) {
    	while(tmp % j == 0) {
          	a[j]++;
       		tmp /= j;
        }
    }
  }
  long cnt = 1;
  for(int i = 2; i <= n; i++) {
    cnt *= (long)(a[i] + 1);
  	cnt %= (long)(1E9+7);
  }
  cout << cnt << endl;
}