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C - Matrix Reducing

Score : $300$ points

Problem Statement

You are given a matrix $A$ with $H_1$ rows and $W_1$ columns, and a matrix $B$ with $H_2$ rows and $W_2$ columns.

• For all integer pairs $(i, j)$ such that $1 \leq i \leq H_1$ and $1 \leq j \leq W_1$, the element at the $i$-th row and $j$-th column of matrix $A$ is $A_{i, j}$.
• For all integer pairs $(i, j)$ such that $1 \leq i \leq H_2$ and $1 \leq j \leq W_2$, the element at the $i$-th row and $j$-th column of matrix $B$ is $B_{i, j}$.

You may perform the following operations on the matrix $A$ any number of (possibly $0$) times in any order:

• Choose an arbitrary row of $A$ and remove it.
• Choose an arbitrary column of $A$ and remove it.

Determine if it is possible to make the matrix $A$ equal the matrix $B$.

Constraints

• $1 \leq H_2 \leq H_1 \leq 10$
• $1 \leq W_2 \leq W_1 \leq 10$
• $1 \leq A_{i, j} \leq 10^9$
• $1 \leq B_{i, j} \leq 10^9$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$H_1$ $W_1$

$A_{1, 1}$ $A_{1, 2}$ $\ldots$ $A_{1, W_1}$

$A_{2, 1}$ $A_{2, 2}$ $\ldots$ $A_{2, W_1}$

$\vdots$

$A_{H_1, 1}$ $A_{H_1, 2}$ $\ldots$ $A_{H_1, W_1}$

$H_2$ $W_2$

$B_{1, 1}$ $B_{1, 2}$ $\ldots$ $B_{1, W_2}$

$B_{2, 1}$ $B_{2, 2}$ $\ldots$ $B_{2, W_2}$

$\vdots$

$B_{H_2, 1}$ $B_{H_2, 2}$ $\ldots$ $B_{H_2, W_2}$

Output

Print Yes if it is possible to make the matrix $A$ equal the matrix $B$; print No otherwise. Note that the judge is case-sensitive.

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4 5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
2 3
6 8 9
16 18 19

Yes

Removing the $2$-nd column from the initial $A$ results in:

``` 1 3 4 5 6 8 9 10 11 13 14 15 16 18 19 20 ```

Then, removing the $3$-rd row from $A$ results in:

``` 1 3 4 5 6 8 9 10 16 18 19 20 ```

Then, removing the $1$-st row from $A$ results in:

``` 6 8 9 10 16 18 19 20 ```

Then, removing the $4$-th column from $A$ results in:

``` 6 8 9 16 18 19 ```

Now the matrix equals the matrix $B$.
Thus, we can make the matrix $A$ equal the matrix $B$ by repeating the operations, so Yes should be printed.

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3 3
1 1 1
1 1 1
1 1 1
1 1
2

No

Regardless of how we perform the operations, we cannot make the matrix $A$ equal the matrix $B$, so No should be printed.