1990 ACM East Central Regional Programming Contest

Problem 1: Lakes

Source file: prob1.c or prob1.pas
Input file: prob1.in
Output file: prob1.out

The Problem

A region of two-dimensional space is divided by a grid into uniform square cells, each of which represents either "land" or "water".

We are interested in finding the area of a region of horizontally or vertically connected "water" cells totally enclosed by a boundary of "land" cells, given the location of a "water" cell in the region.

Choose a representation, such as a two-dimensional array, in which the basic operations available are to determine whether a cell is "land" or "water", and to move from a cell to any of its neighbors. Assume that you are given the location of an arbitrary "water" cell in the region whose area is required.

Since the area of the "water" region is defined to be the number of cells in it, the most straightforward way to compute the area is to simply count the number of cells in it. Write a program to do this.

The following restrictions and assumptions apply:

Input

line 1 - two integers (i,j) separated by 1 blank which represents the position (row, column) of a "water" cell in the region whose area is to be determined. The input integers will be in character form; two non-blank characters followed by a blank followed by two more characters with the characters in [0, 1, ..., 9]
line 2 - the first row of the grid (<=99 characters, all 1's or 0's) where the first character represents G[1,1], the second G[1,2], the third G[1,3], ...
line 3 - the second row of the grid (<=99 characters, all 1's or 0's) where the first character represents G[2,1], the second G[2,2], the third G[2,3], ...
remaining lines for the remaining rows of the grid

Output

Display on the screen one integer which is the area of the enclosed area of water.

Example

Input

	02 01
	1001101
	0011111
	0001001
	1100011
	1111111
	1100110
	1110111

Interpretation

	  012345678
	0 LLLLLLLLL
	1 LLWWLLWLL
	2 LWWLLLLLL
	3 LWWWLWWLL
	4 LLLWWWLLL
	5 LLLLLLLLL
	6 LLLWWLLWL
	7 LLLLWLLLL
	8 LLLLLLLLL

Output

	12