Chef has started developing interest in playing chess, and was learning how the [Queen] moves.

Chef has an empty $N \times N chessboard. He places a Queen at (X, Y)$ and wonders - What are the number of cells that are under attack by the Queen?

Notes:
The top-left cell is (1, 1), the top-right cell is (1, N), the bottom-left cell is (N,1) and the bottom-right cell is (N, N).
The Queen can be moved any number of unoccupied cells in a straight line vertically, horizontally, or diagonally.
The cell on which the Queen is present, is not said to be under attack by the Queen.

------ Input Format ------

• The first line contains a single integer T - the number of test cases. Then the test cases follow.
• The first and only line of each test case contains three integers N, X and Y, as described in the problem statement.

------ Output Format ------

For each test case, output in a single line, the total number of cells that are under attack by the Queen.

------ Constraints ------

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{6}$
$1 ≤ X, Y ≤ N$

----- Sample Input 1 ------
5
1 1 1
3 2 2
3 2 1
2 2 2
150 62 41

----- Sample Output 1 ------
0
8
6
3
527

----- explanation 1 ------
Test case 1: The only cell on the board is $(1,1)$. Since Queen stands on this cell, it is not under attack.

Test case 2: The Queen can attack the following cells: $\{(1, 1), (1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2), (3, 3)\}$.

Test case 3: The Queen can attack the following cells: $\{(1, 1), (1, 2), (2, 2), (2, 3), (3, 1), (3, 2)\}$.

Test case 4: The Queen can attack the following cells: $\{(1, 1), (1, 2), (2, 1)\}$.

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