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;
void swap(long long int arr[], long long int x, long long int y) {
  long long int temp = arr[x];
  arr[x] = arr[y];
  arr[y] = temp;
}
long long int exponentMod(long long int A, long long int B, long long int C) {
  long long int y;
  if (A == 0) return 0;
  if (B == 0) return 1;
  if (B % 2 == 0) {
    y = exponentMod(A, B / 2, C);
    y = (y * y) % C;
  } else {
    y = A % C;
    y = (y * exponentMod(A, B - 1, C) % C) % C;
  }
  return (long long int)((y + C) % C);
}
int spf[100001];
void sievespf() {
  spf[1] = 1;
  for (int i = 2; i < 100001; i++) {
    spf[i] = i;
  }
  for (int i = 4; i < 100001; i += 2) spf[i] = 2;
  for (int i = 3; i * i < 100001; i++) {
    if (spf[i] == i) {
      for (int j = i * i; j < 100001; j += i)
        if (spf[j] == j) spf[j] = i;
    }
  }
}
void input_arr(long long int arr[], long long int n) {
  for (long long int i = 0; i < n; i++) {
    cin >> arr[i];
  }
}
bool primes[100001];
void seive() {
  memset(primes, true, sizeof(primes));
  primes[0] = false;
  primes[1] = false;
  for (long long int i = 2; i * i <= 100001; i++) {
    if (primes[i]) {
      for (long long int j = 2 * i; j < 100001; j += i) {
        primes[j] = false;
      }
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long int t;
  t = 1;
  seive();
  while (t--) {
    int n;
    cin >> n;
    int arr[n + 1];
    for (int i = 0; i <= n; i++) {
      arr[i] = 100000;
    }
    int count1 = 1;
    for (int i = 1; i <= n; i++) {
      if (primes[i]) {
        arr[i] = count1;
        count1++;
      }
    }
    for (int i = 2; i <= n; i++) {
      if (primes[i]) {
        for (int j = 2 * i; j <= n; j += i) {
          arr[j] = min(arr[i], arr[j]);
        }
      }
    }
    for (int i = 2; i <= n; i++) {
      cout << arr[i] << ' ';
    }
  }
  return 0;
}