Maximal crosses

Problem code: MAXCROSS

The 'Clarification' in the problem statement has been updated on July 2nd at 6:15pm

On the matrix A sized n n, some cells were marked by crosses (X). For each cell (i,j) (with i the row index, j the column index), we define B(i,j) as the maximal number of continuous crosses going across the cell (i,j) in the same horizontal, vertical or diagonal; B(i,j)=0 if A(i,j) is empty ( '.' ). [ Empty cells are marked by '.'] .

Clarification:
Continuous crosses going across cell (i,j) in horizontal direction = x1 + x2 - 1
where x1 = highest possible x such that
j + x - 1<= n and A(i, j ... j + x - 1) are all 'X'
and x2 = highest possible x such that
j - x + 1 > 0 and A(i, j - x + 1...j) are all 'X'

Similarily we can extend the definition for vertical and diagonal directions.

Task

Given matrix A as input, calculate matrix B.

Input

 

  • The first line contains the integer n.
  • Then follow n lines , each containing n characters. The j-th character of the i-th line represents the cell (i,j) of the matrix A, with A(i,j)='X' if it contains a cross, or A(i,j)='.' if it is empty.

 

Output

Output n lines, each contains n integers, the j-th integer of the i-th line shows the value of B(i,j).
(Each integer on a same line must be separated by exactly one space character)

Example

Input:

10
..X....XX.
XX.X..XX.X
.....XX..X
.XXX..X.X.
.....X..XX
....X....X
X.X....XX.
.X...X.X.X
X.X..X....
..XXXXX.XX

Output:

0 0 2 0 0 0 0 3 3 0 
2 2 0 2 0 0 3 3 0 2 
0 0 0 0 0 3 3 0 0 2 
0 3 3 3 0 0 3 0 2 0 
0 0 0 0 0 3 0 0 2 2 
0 0 0 0 3 0 0 0 0 3 
4 0 3 0 0 0 0 2 3 0 
0 4 0 0 0 3 0 3 0 2 
3 0 4 0 0 3 0 0 0 0 
0 0 5 5 5 5 5 0 2 2

Limitations

0<n 1 000

Author: anhdq
Date Added: 4-05-2010
Time Limit: 1 - 1.5 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TEXT, WSPC


Comments

@admin: Could you please tell

jc_ortz @ 15 Jul 2010 12:02 AM

@admin:

Could you please tell me in which test case my solution fail?

thanks.

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