Problem:
Score : 600 points

Problem Statement

Given is an integer N.
Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N.
It can be proved that such a positive integer k always exists.

Constraints

1 \leq N \leq 10^{15}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer in a line.

Sample Input 1

11

Sample Output 1

10

1+2+\cdots+10=55 holds and 55 is indeed a multple of N=11.
There are no positive integers k \leq 9 that satisfy the condition, so the answer is k = 10.

Sample Input 2

20200920

Sample Output 2

1100144

Solution in PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php

/*   INPUT  */
[$N] = fscanf(STDIN, "%d");

$mod = 2*$N;
$k = 1;
$div = 2;
/*   FOR  */
while($k>0){
    if($div % $mod === 0){
        echo $k;
        return;
    }
    $div += 2*($k + 1);
    $k++;
}


?>