training_2003_11_08 - Nearest number

Problem D. Nearest number - 2 ≡

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Author:	A. Klenin	Time limit:	5 sec
Input file:	input.txt	Memory limit:	200 Mb
Output file:	output.txt

Statement

Input is the matrix A of N by N non-negative integers.

A distance between two elements A_i j and A_p q is defined as |i − p| + |j − q|.

Your program must replace each zero element in the matrix with the nearest non-zero one. If there are two or more nearest non-zeroes, the zero must be left in place.

Input file format

Input file contains the number N followed by N² integers, representing the matrix row-by-row.

Output file format

Output file must contain N² integers, representing the modified matrix row-by-row.

Constraints

1 ≤ N ≤ 200, 0 ≤ A_i ≤ 1000000

Sample tests

No.	Input file (`input.txt`)	Output file (`output.txt`)
1	`3 0 0 0 1 0 2 0 3 0`	`1 0 2 1 0 2 0 3 0`