The Attack of Queen solution codechef

The Attack of Queen solution codechef

 

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

Chef has an empty N×NN×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?

Notes: The Attack of Queen solution codechef

  • 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).
  • 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 TT – the number of test cases. Then the test cases follow.
  • The first and only line of each test case contains three integers NNXX and YY, as described in the problem statement.

Output Format The Attack of Queen solution codechef

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

Constraints

  • 1T1041≤T≤104
  • 1N1061≤N≤106
  • 1X,YN1≤X,Y≤N

The Attack of Queen solution codechef 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 The Attack of Queen solution codechef

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)}.

 Solution

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