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}.

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.

Constraints

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

Sample Input 1

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

Sample Output 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.

Sample Input 2

2
0 0
0 0
1 1
1 1

Sample Output 2

Yes

Sample Input 3

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

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分