The Imperfect Sheet

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Being bored with the traps in your secret hideout design, you decided to go for something classical, but always enjoyable  the spinning blade. You ordered a really heavy metal sheet out of which you will cut the blade; a uniform square CbyR grid will be painted on the sheet. You have determined the best shape for the blade  you will first cut a large square consisting of KbyK grid cells, where K ≥ 3. Then, you will cut out the four 1by1 corner cells out of the square to end up with a blade. After determining all this, you started waiting for the sheet to arrive.
When the sheet arrived, you were shocked to find out that the sheet had imperfections in it! You expected each cell to have mass D, but it turned out that the mass can vary a bit because of differences in thickness. This is bad because you want to insert a shaft exactly in the center of the blade and spin it very fast, so the center of mass of the blade must be exactly in its center as well. The definition of the center of mass of a flat body can be found below.
Given the grid and the mass of each cell, what is the largest possible size of the blade you can make so that the center of mass is exactly in its center?
Input
The first line of the input gives the number of test cases, T. T test cases follow. Each one starts with a line containing 3 integers: R, C and D — the dimensions of the grid and the mass you expected each cell to have. The next R lines each contain C digits wij each, giving the differences between the actual and the expected mass of the grid cells. Each cell has a uniform density, but could have an integer mass between D + 0 and D + 9, inclusive.
Output
For each test case, output one line containing "Case #x: K", where x is the case number (starting from 1) and K is the largest possible size of the blade you can cut out. If no acceptable blade of size at least 3 can be found, print "IMPOSSIBLE" instead.
Constraints
 1 ≤ T ≤ 20
 0 ≤ wij ≤ 9
 3 ≤ R ≤ 500
 3 ≤ C ≤ 500
 1 ≤ D ≤ 106
The size of the input file will not exceed 625KB.
Example
Input: 2 6 7 2 1111111 1122271 1211521 1329131 1242121 1122211 3 3 7 123 234 345 Output: Case #1: 5 Case #2: IMPOSSIBLE
Note
The center of mass of a 2D object is formally defined as a point c. If you compute the sum of (p  c) * mass(p) for all points p in the object, you must get 0. Here, p, c and 0 are twodimensional vectors. This definition also works if you treat each grid cell as a "point", with all of its mass at its center.
In real life, you could place your finger under a flat object's center of mass, and balance that object on your finger. It would not fall.
To illustrate with an example, the only blade that is possible to cut out in the second sample test case, the 3x3 blade created by cutting away the corners, has its center of mass at the point (1.54, 1.46), where we assume the bottomleft corner of the sheet has coordinates (0, 0), and the coordinates grow right and up, respectively. This is verified by checking the following equality: (1.04, 0.04) * 9 + (0.04, 1.04) * 9 + (0.04, 0.04) * 10 + (0.04, 0.96) * 11 + (0.96, 0.04) * 11 = (0, 0).
Author:  rajat503 
Tags  rajat503 
Date Added:  7022015 
Time Limit:  3 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS 
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