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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;

public class Hello
{
    private const int MOD_N = 1000000000 + 7;

    public static void Main()
    {
        var a = new int[3][];
        for (int i = 0; i < a.Length; ++i)
        {
            var t = Console.ReadLine().Split(' ');
            var a_ = new int[t.Length];
            for (int j = 0; j < a_.Length; ++j)
                a_[j] = int.Parse(t[j]);
            a[i] = a_;
        }

        var n = int.Parse(Console.ReadLine());
        var b = new int[n];
        for (int i = 0; i < b.Length; ++i)
            b[i] = int.Parse(Console.ReadLine());

        var c = new bool[3][];
        for (int i = 0; i < c.Length; ++i)
            c[i] = new bool[3];

        foreach (var b_ in b)
        {
            for (int i = 0; i < a.Length; ++i)
            {
                var a_ = a[i];
                for (int j = 0; j < a_.Length; ++j)
                {
                    if (a_[j] == b_)
                    {
                        c[i][j] = true;
                        i = a.Length;
                        break;
                    }
                }
            }
        }

        foreach (var c_ in c)
        {
            var result = true;
            foreach (var c__ in c_)
            {
                if (!c__)
                {
                    result = false;
                    break;
                }
            }
            if (result)
            {
                Console.WriteLine("Yes");
                return;
            }
        }

        for (int i = 0; i < 3; ++i)
        {
            var result = true;
            for (int j = 0; j < 3; ++j)
            {
                if (!c[j][i])
                {
                    result = false;
                    break;
                }
            }
            if (result)
            {
                Console.WriteLine("Yes");
                return;
            }
        }

        var result3 = true;
        for (int i = 0; i < 3; ++i)
        {
            if (!c[i][i])
            {
                result3 = false;
                break;
            }
        }
        if (result3)
        {
            Console.WriteLine("Yes");
            return;
        }

        var result2 = true;
        for (int i = 0; i < 3; ++i)
        {
            if (!c[2 - i][2 - i])
            {
                result2 = false;
                break;
            }
        }
        if (result2)
        {
            Console.WriteLine("Yes");
            return;
        }

        Console.WriteLine("No");
    }

    private static int GCD(int a, int b) => a > b ? GCD_impl(a, b) : GCD_impl(b, a);
    private static int GCD_impl(int a, int b) => b == 0 ? a : GCD_impl(b, a % b);
    private static long LCM(int a, int b) => (long)a * b / GCD(a, b);

    private static int Comb(int m, int n)
    {
        var t = m - n;
        if (n > t)
            n = t;

        long numerator = 1;
        for (int i = 0; i < n; ++i)
        {
            numerator *= m - i;
            numerator %= MOD_N;
        }
        long denominator = 1;
        for (; n != 0; --n)
        {
            denominator *= n;
            denominator %= MOD_N;
        }

        var inv_denominator = ModInv((int)denominator, MOD_N);
        var ret = (int)(numerator * inv_denominator % MOD_N);

        return ret >= 0 ? ret : ret + MOD_N;
    }

    private static int ModInv(int a, int m)
    {
        int b = m, x = 1, y = 0;
        while (b != 0)
        {
            var t = a / b;
            a -= t * b;
            Swap(ref a, ref b);
            x -= t * y;
            Swap(ref x, ref y);
        }
        x %= m;
        return x >= 0 ? x : x + m;
    }

    private static void Swap<T>(ref T a, ref T b)
    {
        var t = a;
        a = b;
        b = t;
    }
}