Binary Matrix Construction for Optimization

Given an integer (D) and an (n \times m) real matrix (A = [a_{ij}]) where (0 \le a_{ij} \le D), your task is to construct an (n \times m) binary matrix (B = [b_{ij}]) with each element being either 0 or 1. For the provided matrices (A) and (B), two measures are computed as follows:

[ p_1 = \max \left{ \max_{1 \le j \le m} \left| \sum_{i=1}^n \left(b_{ij}-\frac{a_{ij}}{D}\right) \right|, \quad \max_{1 \le i \le n} \left| \sum_{j=1}^m \left(b_{ij}-\frac{a_{ij}}{D}\right) \right| \right} ]

[ p_2 = \max_{1 \le i \le n,, 1 \le j \le m} \left| b_{ij} + b_{i-1,j} + b_{i,j-1} + b_{i-1,j-1} - \frac{a_{ij}+a_{i-1,j}+a_{i,j-1}+a_{i-1,j-1}}{D} \right| ]

Your goal is to choose the matrix (B) so that either (p_1) or (p_2) is as small as possible. In this problem, you only need to output any valid binary matrix (B) that meets the constraints.

inputFormat

The first line contains three numbers: an integer (D), and two integers (n) and (m) representing the number of rows and columns of matrix (A), respectively.

Each of the next (n) lines contains (m) real numbers separated by spaces, representing the matrix (A). It is guaranteed that (0 \le a_{ij} \le D) for all valid (i) and (j).

outputFormat

Output (n) lines, each containing (m) integers (either 0 or 1) separated by a space, representing the binary matrix (B).

sample

5 2 3
0 2.5 5
1 3 4

0 0 0
0 0 0