ROBOTGRI  Robots on a grid
You have recently made a grid traversing robot that can find its way from the top left corner of a grid to the bottom right corner. However, you had forgotten all your AI programming skills, so you only programmed your robot to go rightwards and downwards (that's after all where the goal is). You have placed your robot on a grid with some obstacles, and you sit and observe. However, after a while you get tired of observing it getting stuck, and ask yourself "How many paths are there from the start position to the goal position?", and "If there are none, could the robot have made it to the goal if it could walk upwards and leftwards?" So you decide to write a program that, given a grid of size n x n with some obstacles marked on it where the robot cannot walk, counts the dierent ways the robot could go from the top left corner s to the bottom right t, and if none, tests if it were possible if it could walk up and left as well. However, your program does not handle very large numbers, so the answer should be given modulo 2^{31}  1.
Input
On the first line is one integer, 1 < n <= 1000. Then follows n lines, each with n characters, where each character is one of '.' and '#', where '.' is to be interpreted as a walkable tile and '#' as a nonwalkable tile. There will never be a wall at s, and there will never be a wall at t.
Output
Output one line with the number of dierent paths starting in s and ending in t (modulo 2^{31}  1) or THE GAME IS A LIE if you cannot go from s to t going only rightwards and downwards but you can if you are allowed to go left and up as well, or INCONCEIVABLE if there simply is no path from s to t.
Example
Input: ..... #..#. #..#. ...#. ..... Output: 6
hide comments
aniket_7781:
20210625 11:59:51
I was so excited ...that I made so many silly mistakes...n read problem carefully we don't need to count no of ways by going left n upwards...just down n right for dp n bfs ;) 

amanjainnnn:
20210508 12:31:19
SPOJ NEVER FAILS TO IMPRESS


jenishmonpara:
20200420 15:35:48
My first AC in one go in SPOJ.


nagaraj41:
20200413 08:38:54
just google 2^31 1 and copy paste if you are having issues. Also take care of the output format. i typed "THIS" instead of "THE" resulting in WA's. felt foolish. 

coolio_1:
20200219 17:16:39
Multiple WA due to MOD.


pas7582128:
20191230 19:06:44
AC in one go. 

sudhiawasthi:
20191114 11:10:24
For people getting WA on test case 18, check how your bfs works for the first row and first column, the invalid moves are causing WA. 

wingman__7:
20191109 18:09:41
easy BFS problem, use queue no need for recursion 

ekta_9:
20191109 07:24:47
i am using top down dp here but still getting TLE .whyyyyy? 

darshanpatel:
20190522 07:29:26
You have to actually print "THE GAME IS A LIE " or " INCONCEIVABLE" (without quotes) ! Take care of modulo by typecasting 1<<31 to ((long long)1<<31). 
Added by:  Krzysztof Lewko 
Date:  20111005 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Nordic programming contest 