OR Matrix

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You are given a matrix of integers $A$ with $N$ rows (numbered $1$ through $N$) and $M$ columns (numbered $1$ through $M$). Each element of this matrix is either $0$ or $1$. A *move* consists of the following steps:  Choose two different rows $r_1$ and $r_2$ or two different columns $c_1$ and $c_2$.  Apply the bitwise OR operation with the second row/column on the first row/column. Formally, if you chose two rows, this means you should change $A_{r_1, k}$ to $A_{r_1, k} \lor A_{r_2, k}$ for each $1 \le k \le M$; if you chose two columns, then you should change $A_{k, c_1}$ to $A_{k, c_1} \lor A_{k, c_2}$ for each $1 \le k \le N$. For each element of the matrix, compute the minimum number of moves required to make it equal to $1$ or determine that it is impossible. Note that these answers are independent, i.e. we are starting with the initial matrix for each of them. ### Input  The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.  The first line of each test case contains two spaceseparated integers $N$ and $M$.  $N$ lines follow. For each $i$ ($1 \le i \le N$), the $i$th of these lines contains $M$ integers $A_{i, 1}, A_{i, 2}, \dots, A_{i, M}$ NOT separated by spaces. ### Output For each test case, print $N$ lines. For each valid $i$, the $i$th of these lines should contain $M$ spaceseparated integers; for each valid $j$, the $j$th of these integers should be the minimum number of moves required to make $A_{i, j}$ equal to $1$, or $1$ if it is impossible. ###Constraints  $1 \le T \le 100$  $1 \le N, M \le 1,000$  $A_{i, j} \in \{0, 1\}$ for each valid $i, j$  the sum of $N \cdot M$ for all test cases does not exceed $1,000,000$ ### Example Input ``` 1 3 3 010 000 001 ``` ### Example Output ``` 1 0 1 2 1 1 1 1 0 ```Author:  kingofnumbers 
Editorial  https://discuss.codechef.com/problems/ORMATRIX 
Tags  array, cook96, implementation, kingofnumbers, simple 
Date Added:  20072018 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, 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, kotlin, PERL6, TEXT, SCM chicken, CLOJ, COB, FS 
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