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 c[200000], a[200000];
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  fill(c, c + 200000, 1);
  long long n;
  cin >> n;
  c[0] = c[1] = 0;
  for (long long i = 2; i <= 150000; i++) {
    if (c[i]) {
      if (i * 1LL * i <= 150000) {
        for (long long j = i * i; j <= 150000; j += i) {
          c[j] = 0;
        }
      }
    }
  }
  long long f = 0;
  for (long long i = 2; i <= n; i++) {
    if (a[i]) continue;
    f++;
    for (long long j = i; j <= n; j += i) {
      a[j] = f;
    }
  }
  for (long long i = 2; i <= n; i++) {
    cout << a[i] << ' ';
  }
  return 0;
}