STORE  Storekeeper
The floor of a store is a rectangle divided into n*m square fields. Two fields are adjacent, if they have a common side. A parcel lays on one of the fields. Each of the remaining fields is either empty, or occupied by a case, which is too heavy to be moved by a storekeeper. The storekeeper has to shift the parcel from the starting field P to the final field K. He can move on the empty fields, going from the field on which he stands to a chosen adjacent field. When the storekeeper stays on a field adjacent to the one with the parcel he may push the parcel so that if moves to the next field (i.e. the field on the other side of the parcel), assuming condition that there are no cases on this field.
Task
Write a program, which:
 reads from the standard input a store scheme, a starting position of the storekeeper and a final position of the parcel,
 computes minimal number of the parcel shifts through borders of fields, which are necessary to put the parcel in the final position or decides that it is impossible to put the parcel there,
 writes the result into the standard output.
Input
The number of test cases t is in the first line of input, then t test cases follow separated by an empty line. In the first line of each test case two positive integers separated by a single space, n,m<=100, are written. These are dimensions of the store. In each of the following n lines there appears one mletter word made of letters S, M, P, K, w. A letter on ith position in jth word denotes a type of the field with coordinates (i,j) and its meaning is following:
 S  case,
 M  starting position of the storekeeper,
 P  starting position of the parcel,
 K  final position of the parcel,
 w  empty field.
Each letter M, P and K appears in the test case exactly once.
Output
Your program should write to the standard output for each test case:
 exactly one word NO if the parcel cannot be put on the target field,
 exactly one integer, equal to the minimal number of the parcel shifts through borders of the fields, necessary to put a parcel on a final position, if it is possible to put the parcel there.
Example
Sample input: 1 10 12 SSSSSSSSSSSS SwwwwwwwSSSS SwSSSSwwSSSS SwSSSSwwSKSS SwSSSSwwSwSS SwwwwwPwwwww SSSSSSSwSwSw SSSSSSMwSwww SSSSSSSSSSSS SSSSSSSSSSSS Sample output 7
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Sun Zehao:
20110807 15:04:11
What's the maximum of t? 

:D:
20101209 14:18:22
Also see problem CURSE 

Janusz Wróbel:
20100915 17:51:12
Ok, my mistake  I see the way now.


Janusz Wróbel:
20100913 11:41:37
How can we move the parcel to the end position in Sample Case? I think it's impossible, because it'll block the way for keeper. 
Added by:  Piotr Łowiec 
Date:  20040913 
Time limit:  7s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel Pentium G860 3GHz) 
Languages:  All 
Resource:  6th Polish Olympiad in Informatics, stage 3 