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.

11

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 $k = 10$.

20200920

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