Problem:
Score : 200 points

Problem Statement

We have a bingo card with a 3\times3 grid. The square at the i-th row from the top and the j-th column from the left contains the number A_{i, j}.

The MC will choose N numbers, b_1, b_2, \cdots, b_N. If our bingo sheet contains some of those numbers, we will mark them on our sheet.

Determine whether we will have a bingo when the N numbers are chosen, that is, the sheet will contain three marked numbers in a row, column, or diagonal.

Constraints

All values in input are integers.

1 \leq A_{i, j} \leq 100

A_{i_1, j_1} \neq A_{i_2, j_2} ((i_1, j_1) \neq (i_2, j_2))

1 \leq N \leq 10

1 \leq b_i \leq 100

b_i \neq b_j (i \neq j)

Input

Input is given from Standard Input in the following format:

A_{1, 1} A_{1, 2} A_{1, 3}
A_{2, 1} A_{2, 2} A_{2, 3}
A_{3, 1} A_{3, 2} A_{3, 3}
N
b_1
\vdots
b_N

Output

If we will have a bingo, print Yes; otherwise, print No.

Sample Input 1

84 97 66
79 89 11
61 59 7
7
89
7
87
79
24
84
30

Sample Output 1

Yes

We will mark A_{1, 1}, A_{2, 1}, A_{2, 2}, A_{3, 3}, and complete the diagonal from the top-left to the bottom-right.

Sample Input 2

41 7 46
26 89 2
78 92 8
5
6
45
16
57
17

Sample Output 2

No

We will mark nothing.

Sample Input 3

60 88 34
92 41 43
65 73 48
10
60
43
88
11
48
73
65
41
92
34

Sample Output 3

Yes

We will mark all the squares.

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>

int main(){
    std::vector< std::vector< int > > A(3, std::vector< int >(3));
    for(int i=0; i<3; i++){
        for(int j=0; j<3; j++){
            std::cin >> A[i][j];
        }
    }
    int N;
    std::cin >> N;
    std::vector< int > B(N);
    for(int i=0; i<N; i++){
        std::cin >> B[i];
    }
    
    std::vector< std::vector< bool > > exist(3, std::vector< bool >(3));
    for(int i=0; i<3; i++){
        for(int j=0; j<3; j++){
            exist[i][j] = false;
        }
    }
    
    for(int bc=0; bc<N; bc++){
        for(int aic=0; aic<3; aic++){
            for(int ajc=0; ajc<3; ajc++){
                if(B[bc] == A[aic][ajc]){ exist[aic][ajc] = true; }
            }
        }
    }
    
    bool bingo = false;
    for(int i=0; i<3; i++){
        if(exist[i][0] && exist[i][1] && exist[i][2]){ bingo = true; }
        if(exist[0][i] && exist[1][i] && exist[2][i]){ bingo = true; }
    }
    if(exist[0][0] && exist[1][1] && exist[2][2]){ bingo = true; }
    if(exist[2][0] && exist[1][1] && exist[0][2]){ bingo = true; }

    if(bingo){
        std::cout << "Yes" << std::endl;
    }else{
        std::cout << "No" << std::endl;
    }
}