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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

n = gets.to_i

(1..n).each do |i|
  num = 8 * i * n + 1
  sq = Math.sqrt(num).to_i
  if num % sq == 0
    puts (sq.to_i - 1) / 2
    return
  end
end