RIOI_2_3 - Path of the righteous man


 You are given N*N matrix A filled with integers, which represents map of country "What" ("What" ain't no country I ever heard of) . Our hero is called Brett. Brett has many enemies, namely Jules and Vincent (Jules doesn't like him because he said "what" too many times), but his biggest enemy is Marcellus Wallace, because Brett treated him like a male dog treats female dog. And Marcellus most certainly does not look like a female dog. 

But Brett cannot sit at home all day enjoying his Big Kahuna burgers, he has to go from cell (sx, sy) to cell (ex, ey).

From cell (x, y) Bret can go to (x+1, y), (x, y+1), (x-1, y), (x, y-1).

If A[x][y] = S, we say that this cell is property of mafia boss S. When Brett visits cell (x, y), and has not yet apologised to boss A[x][y], then he apologizes, after that he can visit any cell controlled by A[x][y] without apologizing. Brett does not like to apologise ( because there is always chance to hear Ezekiel 25 17 ), so he asks you to find him path which minimizes number of times he has to apologise.

You are given N*N matrix A filled with integers, which represents map of country "What" ("What" ain't no country I ever heard of) . Our hero is called Bret. Bret has many enemies, namely Jules and Vincent (Jules doesn't like him because he said "what" too many times), but his biggest enemy is Marcellus Wallace, because Bret treated him like male dog treats female dog. 

Bret has to go from cell (sx, sy) to cell (ex, ey).
From cell (x, y) Bret can go to (x+1, y), (x, y+1), (x-1, y), (x, y-1).
If A[x][y] = S, we say that this cell is property of mafia boss S. When Bret visits cell (x, y), and has not yet apologised to boss A[x][y], then he apologizes, after that he can visit any cell controlled by A[x][y] without apologizing. Bret does not like to apologise ( because there is always chance to hear Ezekiel 25 17 ), so he asks you to find him path which minimizes number of times he has to apologise.

Constranits: 

N <= 50

0 <= A[i][j] < 10

Input

First line contains number t donating number of testcases. First line of each testcase consists of number N. N lines followscontaining N numbers donating matrix A. After that two lines follow, containing sx, sy and ex, ey.

Output

For each test output number minimal number of times bret has to apologise.

Example

Input:
3
5
0 1 0 2 3
0 2 0 3 1
0 5 0 0 0
0 5 7 8 0
0 0 0 0 0
0 0
0 4 
5
0 1 0 2 3
0 2 0 3 1
0 5 0 0 0
0 5 7 8 0
0 0 0 0 0
0 0
0 2
5
0 1 0 8 3
0 2 0 3 1
0 5 0 0 0
0 5 7 8 9
0 0 0 0 0
0 0
0 3
Output:
3
1
2
Explanation of second test case : Bret can reach cell (0, 2) following path on which each cell is controled by boss 0.
NOTE : If you wish to understand references in problem statement, 
watch movie Pulp Fiction, or this clip http://www.youtube.com/watch?v=aBs3Mu-qous

hide comments
Buda IM (retired): 2016-07-23 10:33:18

Please do not post hints in comments (some people find this very hard to comprehend), read the notes below

aditya730: 2016-01-29 14:24:46

Think it should have been made clear that the value corresponding to the starting position must also be considered while counting the number of times he has to apologise.Costed me a great deal of time.

Sudharsansai: 2015-03-25 20:09:18

Silly mistake costed a WA :( ...Anyway a nice question ...

Viktor Fonic: 2012-11-17 14:55:06

This is really great task and even better task description, Buda! :)

Rocker3011: 2012-11-16 05:04:42

it is funny how just memory some sums and cutting to half a for can take your time from TLE to AC

:D: 2012-11-10 15:34:43

Buda IM. No vulgar words in problem description! Please rephrase the statement.

And yes, I know you're referring to "Pulp Fiction", but we must keep our site kid friendly :)

Re:
Bit** is not vulgarity, but fine, you can return it now

Re Re:
It is in context, but that was nicely done. Thank you for your understanding.

Last edit: 2012-11-10 18:10:10
Archit Mittal: 2012-11-10 15:34:43

can somebody give some tougher test cases..

Buda IM: I have added one more

Last edit: 2012-11-06 18:42:49

Added by:Buda IM
Date:2012-11-01
Time limit:0.481s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM32-GCC COBOL D-DMD ELIXIR FANTOM GOSU GRV JS-MONKEY NIM OBJC PICO CHICKEN VB.NET
Resource:Own Problem