The ? 1 ? 2 ? ... ? n = k problem

Time Limit: 3000 ms Memory Limit: 65536 KiB

Problem Description

 

Given the following formula, one can set operators '+' or '-' instead of each '?', in order to obtain a given k
? 1 ? 2 ? ... ? n = k

For example: to obtain k = 12 , the expression to be used will be:
- 1 + 2 + 3 + 4 + 5 + 6 - 7 = 12
with n = 7

Input

 

 

The first line is the number of test cases, followed by a blank line.

 

Each test case of the input contains integer k (0<=|k|<=1000000000).

Each test case will be separated by a single line.

Output

 

For each test case, your program should print the minimal possible n (1<=n) to obtain k with the above formula.

Print a blank line between the outputs for two consecutive test cases.

Sample Input

2

12

-3646397

Sample Output

7

2701

Hint

 

Source