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() {
  cout.sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cerr.tie(0);
  cout << setprecision(16);
  int N;
  while (cin >> N) {
    unsigned long long A[N + 2];
    memset(A, 0, sizeof A);
    int first = 1;
    for (unsigned long long(i) = 0ll; (i) < N + 1; (i)++) {
      if (i < 2) continue;
      if (A[i]) continue;
      for (int U = i; U <= N; U += i) {
        if (A[U]) continue;
        A[U] = first;
      }
      first++;
    }
    for (int i = 2; i <= N; i++) cout << A[i] << " ";
    cout << endl;
  }
}