Kata

Task

Let's define a hole of size n as a matrix which is built as follows.

• Its elements are in range [1..n^2].
• The matrix is filled by rings, from the outwards the innermost.
• Each ring is filled with numbers in the following way:
• the first number is written in the top left corner;
• the second number is written in the top right corner;
• the third number is written in the bottom right corner;
• the fourth number is written in the bottom left corner;
• each next number is written next to the number written 4 steps before it, until the ring is filled.

The matrix is constructed when all numbers are written. Given the size of the hole, return the number written at (a, b).

Example

For n = 4, a = 1, b = 1, the output should be 13.

The hole looks like this:

[
[ 1,  5,  9,  2],
[12, 13, 14,  6],
[ 8, 16, 15, 10],
[ 4, 11,  7,  3],
]
The element at (1, 1) is 13.

For n = 5, a = 3, b = 2, the output should be 23.

The hole looks like this:

[
[ 1,  5,  9, 13,  2],
[16, 17, 21, 18,  6],
[12, 24, 25, 22, 10],
[ 8, 20, 23, 19, 14],
[ 4, 15, 11,  7,  3],
]
The element at (3, 2) is 23.

Input/Output

• [input] integer n

Matrix size, 1 ≤ n ≤ 100.

• [input] integer a

Row number, 0 ≤ a ≤ n - 1.

• [input] integer b

Column number, 0 ≤ b ≤ n - 1.

• [output] an integer

The hole[a][b]