## Table of Contents

**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 NÃ—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**

1â‰¤Tâ‰¤104

1â‰¤Nâ‰¤106

1â‰¤X,Yâ‰¤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). 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)}.

**SOLUTION**

**Program: The Attack of Queen Solution Codechef** in Python

```
t=int(input())
for i in range(t):
n,x,y=map(int,input().split())
q=n-x+x-1+n-y+y-1
a=min(x-1,y-1)
b=min(x-1,n-y)
c=min(n-x,y-1)
d=min(n-x,n-y)
print(q+a+b+c+d)
```

**Program: The Attack of Queen Solution Codechef** in C++

```
#include <bits/stdc++.h>
#include <math.h>
using namespace std;
int main(){
int t;
cin>>t;
while(t--){
long n,x,y;
cin>>n>>x>>y;
cout<<2*n-2 +
min(abs(1-x),(abs(1-y)))+
min(abs(n-x),(abs(n-y)))+
min(abs(1-x),(abs(n-y)))+
min(abs(n-x),(abs(1-y)));
cout<<endl;
}
return 0;
}
```

**Program: The Attack of Queen Solution Codechef** in Java

```
import java.util.*;
import java.lang.*;
import java.io.*;
class Codechef
{ public static void main (String[] args) throws java.lang.Exception
{
Scanner sc=new Scanner(System.in);
int t=sc.nextInt();
for(int i=0;i<t;i++){
int n=sc.nextInt();
int x=sc.nextInt();
int y=sc.nextInt();
int sum=2*(n-1);
sum=sum+Math.min(x,y)+Math.min(n-x,n-y);
sum=sum+Math.min(x-1,n-y)+Math.min(y-1,n-x);
System.out.println(sum-1);
}
}
}
```

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