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