| Queen |
The game of Chess has several pieces with curious movements. One of them is the Queen, which can move any number of squares in any direction: in the same line, in the same column or in any of the diagonals, as illustrated by the figure below (black dots represent positions the queen may reach in one move):
The great Chess Master Kary Gasparov invented a new type of chess problem: given the position of a queen in an empty standard chess board (that is, an 8 x 8 board) how many moves are needed so that she reaches another given square in the board?
Kary found the solution for some of those problems, but is having a difficult time to solve some others, and therefore he has asked that you write a program to solve this type of problem.
The input contains several test cases. The only line of each test case contains four integers X1, Y1, X2 and Y2 (1 ≤ X1, Y1, X2, Y2 ≤ 8). The queen starts in the square with coordinates (X1, Y1), and must finish at the square with coordinates (X2, Y2). In the chessboard, columns are numbered from 1 to 8, from left ro right; lines are also numbered from 1 to 8, from top to bottom. The coordinates of a square in line X and column Y are (X, Y).
The end of input is indicated by a line containing four zeros, separated by spaces.
For each test case in the input your program must print a single line, containing an integer, indicating the smallest number of moves needed for the queen to reach the new position.
4 4 6 2 3 5 3 5 5 5 4 3 0 0 0 0
1 0 2