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 Fortran (gfortran v4.8.4) (judge verdict: Accepted)

program Bingo
    implicit none
    integer(4):: bng(3,3), num
    integer(4):: i,j,k, n
    logical:: is_open(3,3) = .false.

    do i=1, 3
        read*, bng(:,i)
    end do

    read*, n

    do i=1, n
        read*, num

        do j=1,3
            do k=1,3
                if (bng(k,j) == num) is_open(k,j) = .true.  
            end do
        end do
    end do

    if (check_bingo(is_open)) then
        print*, 'Yes'
    else
        print*, 'No'
    end if

    contains
    function check_bingo(is_open) result(is_bingo)
        integer(4):: i,j
        logical:: is_open(3,3), is_bingo

        is_bingo = .false.

        do i=1, 3
            if (is_open(1,i) .and. is_open(2,i) .and. is_open(3,i)) is_bingo = .true.
            if (is_open(i,1) .and. is_open(i,2) .and. is_open(i,3)) is_bingo = .true.
        end do

        if (is_open(1,1) .and. is_open(2,2) .and. is_open(3,3)) is_bingo = .true.
        if (is_open(1,3) .and. is_open(2,2) .and. is_open(3,1)) is_bingo = .true.
        
    end function
end program Bingo