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.

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer in a line.

Constraints

• $1 \leq N \leq 10^{15}$
• All values in input are integers.

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

见题面 Input 部分

见题面 Output 部分