$N$puzzle is a puzzle
that goes by many names and has many variants. In this problem
we will use the $15$puzzle. It consists of a
$4$by$4$ grid of sliding squares where one
square is missing. The squares are labeled with uppercase
letters ’A’ through ’O’, with the desired layout as
follows:
It can be useful (for example, when solving the puzzle using
a computer) to define the "scatter" of a puzzle as the sum of
distances between each square’s current position and its
position in the desired layout. The distance between two
squares is their Manhattan distance (the absolute value of the
sum of differences between the two rows and the two
columns).
Write a program that calculates the scatter of the given
puzzle.
Input
Four lines of input contain four characters each,
representing the state of the puzzle.
Output
Output the scatter of the puzzle on a single line.
Sample Input 1 
Sample Output 1 
ABCD
EFGH
IJKL
M.NO

2

Sample Input 2 
Sample Output 2 
.BCD
EAGH
IJFL
MNOK

6
