#10025The ? 1 ? 2 ? ... ? n = k problem

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 an 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.

2

12

-3646397

7

2701