Ada Matrix

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###Read problems statements in [Hindi](http://www.codechef.com/download/translated/COOK102/hindi/ADAMTR.pdf), [Mandarin Chinese](http://www.codechef.com/download/translated/COOK102/mandarin/ADAMTR.pdf), [Russian](http://www.codechef.com/download/translated/COOK102/russian/ADAMTR.pdf), [Vietnamese](http://www.codechef.com/download/translated/COOK102/vietnamese/ADAMTR.pdf) and [Bengali](http://www.codechef.com/download/translated/COOK102/bengali/ADAMTR.pdf) as well. Ada has two matrices $A$ and $B$, each with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). Ada may perform the following operation any number of times (including zero): choose an integer $i$ ($1 \le i \le N$), then swap row $i$ and column $i$ in matrix $A$. (Formally, for each valid $j$, she swaps $A_{i, j}$ with $A_{j, i}$.) Is it possible to transform matrix $A$ into matrix $B$? ### 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 a single integer $N$.  $N$ lines follow. For each $i$ ($1 \le i \le N$), the $i$th of these lines contains $N$ spaceseparated integers $A_{i, 1}, A_{i, 2}, \ldots, A_{i, N}$.  $N$ more lines follow. For each $i$ ($1 \le i \le N$), the $i$th of these lines contains $N$ spaceseparated integers $B_{i, 1}, B_{i, 2}, \ldots, B_{i, N}$. ### Output For each test case, print a single line containing the string `"Yes"` if it is possible to transform $A$ into $B$ or `"No"` if it is impossible (without quotes). ### Constraints  $1 \le T \le 10^{5}$  $1 \le N \le 2^{10}$  $1 \le A_{i, j}, B_{i, j} \le 10^9$ for each valid $i, j$  the sum of $N^2$ over all test cases does not exceed $3 \cdot 10^{6}$ ### Example Input ``` 1 3 1 2 3 4 5 6 7 8 9 1 2 7 4 5 8 3 6 9 ``` ### Example Output ``` Yes ``` ### Explanation **Example case 1:** We can swap the second row with the second column and in the resulting matrix, swap the first row with the first column.Author:  alei 
Editorial  https://discuss.codechef.com/problems/ADAMTR 
Tags  2sat, alei, dfs, graphtheory 
Date Added:  14012019 
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, PYP3, CLOJ, COB, FS 
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