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 <string>
#include <vector>
#include <queue>
#include <map>
#include <algorithm>

using namespace std;
typedef long long ll;

int main(int argc, const char * argv[]) {
    vector<vector<int>> A(3, vector<int>(3, 0));
    map<int, int> b;
    for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
            int a; cin >> a;
            A[i][j] = a;
            b[a] = 0;
        }
    }
    int N; cin >> N;
    for (int i = 0; i < N; i++) {
        int x; cin >> x;
        b[x] = 1;
    }
    
    //horizontal
    for (int i = 0; i < 3; i++) {
        bool tmp_flag = true;
        for (int j = 0; j < 3; j++) {
            if (b[A[i][j]] != 1) {
                tmp_flag = false;
                break;
            }
        }
        if (tmp_flag) {
            cout << "Yes" << endl;
            return 0;
        }
    }
    // vertical
    for (int i = 0; i < 3; i++) {
        bool tmp_flag = true;
        for (int j = 0; j < 3; j++) {
            if(b[A[j][i]] != 1) {
                tmp_flag = false;
                break;
            }
        }
        if (tmp_flag) {
            cout << "Yes" << endl;
            return 0;
        }
    }
    bool tmp_flag = (b[A[0][0]] == 1 && b[A[1][1]] == 1 && b[A[2][2]] == 1);
    tmp_flag = tmp_flag || (b[A[2][0]] == 1 && b[A[1][1]] == 1 && b[A[2][0]] == 1);
    if (tmp_flag) {
        cout << "Yes" << endl;
        return 0;
    }
    cout << "No" << endl;
    return 0;
}