Problem: You're given an integer n. For every integer i from 2 to n, assign a positive integer a_i such that the following conditions hold:

  * For any pair of integers (i,j), if i and j are coprime, a_i ≠ a_j. 
  * The maximal value of all a_i should be minimized (that is, as small as possible). 



A pair of integers is called [coprime](https://en.wikipedia.org/wiki/Coprime_integers) if their [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) is 1.

Input

The only line contains the integer n (2 ≤ n ≤ 10^5).

Output

Print n-1 integers, a_2, a_3, …, a_n (1 ≤ a_i ≤ n). 

If there are multiple solutions, print any of them.

Examples

Input


4


Output


1 2 1 

Input


3


Output


2 1

Note

In the first example, notice that 3 and 4 are coprime, so a_3 ≠ a_4. Also, notice that a=[1,2,3] satisfies the first condition, but it's not a correct answer because its maximal value is 3.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
long long cmp(long long n) {
  long long flag = 1, i;
  if (n == 2) {
    return 1;
  }
  for (i = 2; i <= sqrt(n); i++) {
    if (n % i == 0) {
      flag = i;
      break;
    }
  }
  return flag;
}
int main() {
  std::ios::sync_with_stdio(false);
  long long x, y, i, j;
  while (cin >> x) {
    map<long long, long long> mm;
    mm.clear();
    for (i = 2, j = 1; i <= x; i++) {
      y = cmp(i);
      if (y == 1) {
        mm[i] = j;
        cout << j << " ";
        j++;
      } else {
        cout << mm[y] << " ";
      }
    }
    cout << endl;
  }
}