P25849 [AtCoder] Matrix Reducing
普及-
题目描述

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.

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.

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.

Sample Input 1

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

Sample Output 1

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.

Sample Input 2

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

Sample Output 2

No

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

输入格式

见题面 Input 部分

输出格式

见题面 Output 部分

样例输入
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
样例输出
Yes