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:
(function () {
    var read = {
        number: function () {
            return +readline();
        },
        arr: function (divider) {
            return readline().split(divider ? divider : '');
        },
        arrNumber: function (divider) {
            return readline()
                .split(divider ? divider : '')
                .map(item => +item);
        }
    };

    var n = read.number();
    var res = '';
    var idx = [];
    var arr = [];
    var index = 1;
    for(var i = 2 ; i <= n; i++) {
        var c = true;
        for(var j = 2; j <= Math.floor(i / 2); j++) {
            if(i % j === 0) {
                c = false;
                break;
            }
        }
        if(c) {
            var tmp = i;
            idx[tmp - 2] = index;
            while(tmp + i <= n) {
                tmp += i;
                idx[tmp - 2] = index;
            }
            index++;
        }
    }
    
    print(idx.join(' '));
}());