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;
int main() {
  int n;
  cin >> n;
  if (n == 2) {
    cout << 1 << endl;
  } else {
    int z = 0;
    vector<bool> mark(n, false);
    vector<int> ans(n + 1, 0);
    for (int i = 2; i <= n; i++) {
      if (mark[i] == false) {
        if (i == 2)
          z = 2;
        else if (i == 3)
          z = 1;
        else
          z++;
        ans[i] = z;
        for (int j = 2 * i; j <= n; j += i) {
          if (mark[j] == false) {
            ans[j] = z;
            mark[j] = true;
          }
        }
      }
      if (i == 3) z += 1;
    }
    for (int i = 2; i <= n; i++) cout << ans[i] << " ";
    cout << endl;
  }
}