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 Java (OpenJDK 1.8.0) (judge verdict: Runtime Error)

public class Main {

	public static void main(String args[]) {
		int n = Integer.parseInt(args[0]);

		int c = 0;

		for (int j = 1; j > 0; j++) {
			c = c + j;

			if (c % n == 0) {
				break;
			}

		}

		System.out.println(c);

	}

}