Centaur
A centaur is a unique chess piece that combines the movements of a knight and a bishop. It can move in an "L" shape like a knight or diagonally like a bishop.
The diagram below illustrates the possible moves of the centaur, with the centaur itself marked by a circle:
Imagine a chessboard with dimensions n×n. The rows are numbered from 1 to n from top to bottom, and the columns are numbered from 1 to n from left to right. A square located at the intersection of the i-th row and j-th column is denoted as (i, j).
The centaur is positioned on an nxn board at the square (i, j), where 1 ≤ i, j ≤ n. Your task is to determine how many different squares the centaur can move to, based on its movement capabilities.
Input
The first line of each test case specifies the size of the board n (n ≤ 10^9). The second and third lines provide the coordinates of the centaur (i, j) (1 ≤ i, j ≤ n).
Output
For each test case, output the number of distinct squares the centaur can move to.