For a boat on a large body of water, strong currents can be
dangerous, but with careful planning, they can be harnessed to
help the boat reach its destination. Your job is to help in
that planning.
At each location, the current flows in some direction. The
captain can choose to either go with the flow of the current,
using no energy, or to move one square in any other direction,
at the cost of one energy unit. The boat always moves in one of
the following eight directions: north, south, east, west,
northeast, northwest, southeast, southwest. The boat cannot
leave the boundary of the lake. You are to help him devise a
strategy to reach the destination with the minimum energy
consumption.
Input Specification
The lake is represented as a rectangular grid. The first
line of input contains two integers $r$ and $c$, the number of rows and columns in
the grid. The grid has no more than 1000 rows and no more than
1000 columns. Each of the following $r$ lines contains exactly
$c$ characters, each a
digit from 0 to 7 inclusive. The character 0 means the current
flows north (i.e. up in the grid, in the direction of
decreasing row number), 1 means it flows northeast, 2 means
east (i.e. in the direction of increasing column number), 3
means southeast, and so on in a clockwise manner:
The line after the grid contains a single integer
$n$, the number of trips
to be made, which is at most 50. Each of the following
$n$ lines describes a trip
using four integers $rs$,
$cs$, $rd$, $cd$, giving the row and column of the
starting point and the destination of the trip. Rows and
columns are numbered starting with 1.
The line after the grid contains a single integer
$n$, the number of trips
to be made, which is at most 50. Each of the following
$n$ lines describes a trip
using four integers $rs$,
$cs$, $rd$, $cd$, giving the row and column of the
starting point and the destination of the trip. Rows and
columns are numbered starting with 1.
Output Specification
For each trip, output a line containing a single integer,
the minimum number of energy units needed to get from the
starting point to the destination.
Sample Input 1 
Sample Output 1 
5 5
04125
03355
64734
72377
02062
3
4 2 4 2
4 5 1 4
5 3 3 4

0
2
1
