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) Brett 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 apologises, after that he can visit any cell controlled by A[x][y] without apologising. 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 minimises number of times he has to apologise.

Constraints

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 follows containing 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 Brett 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

For the second test case, Brett can reach cell (0, 2) following path on which each cell is controlled by boss 0.

NOTE: If you wish to understand references in problem statement, watch the movie Pulp Fiction, or this clip www.youtube.com/watch?v=aBs3Mu-qous


hide comments
dasher2238: 2023-07-31 14:02:36

bitmask + dfs/bfs

shivameasy: 2022-09-13 19:34:54

Nice question

nadstratosfer: 2018-05-01 19:50:25

Wow, as I was ready to bring out the CPP gimp, one observation pushed the original PyPy code past the green bar. Even raw Python flies now! I find myself one smilin' motherfucker. Cool problem.

Last edit: 2018-05-01 19:58:27
holmesherlock: 2018-01-21 17:51:56

extremely beautiful question:::-)

conquistador: 2017-04-02 20:11:13

i dare you , i double dare you to solve this problem .( pulp fiction reference );

vengatesh15: 2017-02-15 08:00:08

Finally removed from my todo_list after a 4 month.

Buda IM (retired): 2016-07-31 20:02:01

Added support for new languages such as C++14

enigmus: 2016-07-31 12:41:47

Very good problem, but maybe a little too tight time limit.
It would also be nice if you added C++11/C++14 support

mario_92: 2016-07-27 15:59:14

What should be the output for sx==ex and sy==ey?
Please provide some tougher test cases. My code is giving right output for all the test cases mentioned here but still it shows WA. If only I could know the test case for which it does not produce the desired output!

Last edit: 2016-07-27 16:23:47
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


Added by:Buda IM
Date:2012-11-01
Time limit:1s
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