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B - Coloring Matrix

Score : $200$ points

Problem Statement

You are given $N$-by-$N$ matrices $A$ and $B$ where each element is $0$ or $1$.
Let $A_{i,j}$ and $B_{i,j}$ denote the element at the $i$-th row and $j$-th column of $A$ and $B$, respectively.
Determine whether it is possible to rotate $A$ so that $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$.
Here, to rotate $A$ is to perform the following operation zero or more times:

• for every pair of integers $(i, j)$ such that $1 \leq i, j \leq N$, simultaneously replace $A_{i,j}$ with $A_{N + 1 - j,i}$.

Constraints

• $1 \leq N \leq 100$
• Each element of $A$ and $B$ is $0$ or $1$.
• All values in the input are integers.

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Input

The input is given from Standard Input in the following format:

$N$

$A_{1,1}$ $A_{1,2}$ $\ldots$ $A_{1,N}$

$\vdots$

$A_{N,1}$ $A_{N,2}$ $\ldots$ $A_{N,N}$

$B_{1,1}$ $B_{1,2}$ $\ldots$ $B_{1,N}$

$\vdots$

$B_{N,1}$ $B_{N,2}$ $\ldots$ $B_{N,N}$

Output

If it is possible to rotate $A$ so that $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$, print Yes; otherwise, print No.

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3
0 1 1
1 0 0
0 1 0
1 1 0
0 0 1
1 1 1

Yes

Initially, $A$ is :

``` 0 1 1 1 0 0 0 1 0 ```

After performing the operation once, $A$ is :

``` 0 1 0 1 0 1 0 0 1 ```

After performing the operation once again, $A$ is :

``` 0 1 0 0 0 1 1 1 0 ```

Here, $B_{i,j} = 1$ for every pair of integers $(i, j)$ such that $A_{i,j} = 1$, so you should print Yes.

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2
0 0
0 0
1 1
1 1

Yes

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5
0 0 1 1 0
1 0 0 1 0
0 0 1 0 1
0 1 0 1 0
0 1 0 0 1
1 1 0 0 1
0 1 1 1 0
0 0 1 1 1
1 0 1 0 1
1 1 0 1 0

No