Knight Moves

Time limit1sMemory limit128 MB

Summary

For each pair of squares, find the minimum number of knight moves between them on a standard 8 by 8 chessboard.

Level: Medium4 of 10
Topics: BFS, Graph, Shortest path
Solved: No attempts yet

Problem

A friend of yours is doing research on the Traveling Knight Problem (TKP), where you must find the shortest closed tour of knight moves that visits each square of a given set of $n$ squares on a chessboard exactly once. He thinks that the most difficult part of the problem is determining the smallest number of knight moves between two given squares, and that once you have accomplished this, finding the tour would be easy.

Of course, you know that it is the other way around. So you offer to write a program that solves the "difficult" part for him.

Your job is to write a program that takes two squares $a$ and $b$ as input and then determines the number of knight moves on a shortest route from $a$ to $b$ .

Input

The input contains one or more test cases. Each test case consists of one line containing two squares separated by a single space. A square is a string consisting of a letter (a–h) representing the column and a digit (1–8) representing the row on the chessboard. Input continues until end of file.

Output

For each test case, print one line saying "To get from xx to yy takes n knight moves.", where xx is the starting square, yy is the target square, and n is the minimum number of knight moves. The output string is fixed English and must be printed exactly as shown.

Examples1

Example 1

Input

e2 e4
a1 b2
b2 c3
a1 h8
a1 h7
h8 a1
b1 c3
f6 f6

Expected output

To get from e2 to e4 takes 2 knight moves.
To get from a1 to b2 takes 4 knight moves.
To get from b2 to c3 takes 2 knight moves.
To get from a1 to h8 takes 6 knight moves.
To get from a1 to h7 takes 5 knight moves.
To get from h8 to a1 takes 6 knight moves.
To get from b1 to c3 takes 1 knight moves.
To get from f6 to f6 takes 0 knight moves.