The Attack of Queen CodeChef Solution | CodeChef Problem Solution 2022

The Attack of Queen CodeChef Solution | CodeChef Problem Solution 2022

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

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

Solution Click Below:-  CLICK HERE

Notes:

• The top-left cell is (1,1)$(1,1)$, the top-right cell is (1,N)$(1,N)$, the bottom-left cell is (N,1)$(N,1)$ and the bottom-right cell is (N,N)$(N,N)$.

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• 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$T$ - the number of test cases. Then the test cases follow.
• The first and only line of each test case contains three integers N$N$, X$X$ and Y$Y$, 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≤104$1\le T\le {10}^4$
• 1≤N≤106$1\le N\le {10}^6$
• 1≤X,Y≤N$1\le X,Y\le N$

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

Test case 1: The only cell on the board is (1,1)$(1,1)$. 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)}$\{(1,1),(1,2),(1,3),(2,1),(2,3),(3,1),(3,2),(3,3)\}$.

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

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

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