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 JAVA):

Solution:
var row = readline().split(" ").map(function(x) { return parseInt(x); });
var n = row[0];

//var a = readline().split(" ").map(function(x) { return parseInt(x); });

var color = 1;
var res = [];

for(var i = 0; i <= n ; i++) {
    res.push(0);
}

for(var i = 2; i <= n ; i++) {
    var flag = false;
    for(var j = i; j <= n; j+=i) {
        if(res[j] == 0) {
            res[j] = color;
            flag = true;
        }
    }
    if(flag) color++;
}

write(res.slice(2).join(" "));