Problem Statement

Now I'm going to give you all a quiz about grids, fuppii~♪ First, the beginner level, pi!

Tester Fuppy-san lives in a city shaped like an $ N \times N $ grid. Each cell of the grid has a name, with the top-left cell being $ ( 0, 0 ) $. The cell reached by moving $ i $ cells down and $ j $ cells right from there is named $ ( i, j ) $. Individuality for every cell. This is what we call diversity. (Diver-city, since it's a city.)

The current time is $ 0 $. Tester Fuppy-san is at the top-left cell $ (0, 0) $. Tester Fuppy-san is initially facing right.

From here until "game over", a move is made each time the time changes, pii~♪ Let me explain the rules, pi!

• A cell that has been visited once must never be visited again.
• If there is no unvisited cell in any of the four directions, it is "game over" at that point.
• If a cell exists ahead (in the direction currently faced) and it is unvisited, move there.
• Otherwise, keep rotating clockwise until an unvisited cell is ahead, and once an unvisited cell is directly ahead, move there.

It can be proven that through this series of moves, Tester Fuppy-san visits all cells and reaches "game over".

Here is an example. If $ N = 4 $, the cells are visited in the following order.

0 1 2 3
11 12 13 4
10 15 14 5
9 8 7 6

Now, here is the question (pii omitted). At what time does Tester Fuppy-san visit the cell $ ( I, J ) $, pi?

Input

$Q$
$N_0\ I_0\ J_0$
$\cdots$
$N_{Q-1}\ I_{Q-1}\ J_{Q-1}$

This problem has multiple test cases. The $ 1 $st line contains the number of test cases $ Q $ as a single integer. Each of the following $ Q $ lines, from the $ 2 $nd line onward, contains the side length of the grid $ N_i $, the vertical position $ I_i $ and the horizontal position $ J_i $ of the cell in question, separated by spaces.

Constraints

• $ 1 \leq Q \leq 100 $
• $ 1 \leq N_i \leq 10 ^ 9 $
• $ 0 \leq I_i < N $
• $ 0 \leq J_i < N $

Output

$t_0$
$\cdots$
$t_{Q-1}$

Sample

1
2 1 1

2

0 1
3 2