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;
vector<int> vv1;
int lim = 1000000;
bool prime[1000000];
void sieve() {
  memset(prime, true, sizeof(prime));
  prime[0] = prime[1] = false;
  for (int i = 2; i * i < lim; i++) {
    if (prime[i]) {
      for (int j = i * i; j < lim; j = j + i) {
        prime[j] = false;
      }
    }
  }
  for (int i = 0; i < lim; i++)
    if (prime[i]) vv1.push_back(i);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  sieve();
  long long tt, cn = 0, cn1 = 0, r = 0, l = 0, h = 0;
  tt = 1;
read:
  while (tt--) {
    vector<long long> vec2, vec1, vec, vec3, vec4, vec11;
    vector<pair<long long, long long>> ve;
    double x1, x2, x3, x4, y1, y2, y3, y4;
    long long a, d, b, c, cn = 0, sum = 0, mx = 0, mx1 = 0, cn1 = 0;
    long long arr[100009];
    memset(arr, 0, sizeof(arr));
    cin >> a;
    for (int i = 2; i <= a; i++) {
      if (arr[i] == 0) {
        cn++;
        for (int j = i; j <= a; j += i) arr[j] = cn;
      }
    }
    for (int i = 2; i <= a; i++) cout << arr[i] << " ";
    cout << endl;
  }
  return 0;
}