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 OCaml (4.02.3) (judge verdict: Accepted)

let () =
    let main () =
        let ar = Array.make 101 1024 in
        for i = 0 to 8 do
            Scanf.scanf " %d" (fun a -> ar.(a) <- 1 lsl i)
        done;
        let n = Scanf.scanf " %d" (fun n -> n) in
        let rec loop i map =
            if i = 0 then map else
                let b = Scanf.scanf " %d" (fun b -> b) in
                loop (i - 1) (map lor ar.(b))
        in
        let m = loop n 0 in
        let l = [
            (1 lsl 0) lor (1 lsl 1) lor (1 lsl 2) ;
            (1 lsl 3) lor (1 lsl 4) lor (1 lsl 5) ;
            (1 lsl 6) lor (1 lsl 7) lor (1 lsl 8) ;
            (1 lsl 0) lor (1 lsl 3) lor (1 lsl 6) ;
            (1 lsl 1) lor (1 lsl 4) lor (1 lsl 7) ;
            (1 lsl 2) lor (1 lsl 5) lor (1 lsl 8) ;
            (1 lsl 0) lor (1 lsl 4) lor (1 lsl 8) ;
            (1 lsl 2) lor (1 lsl 4) lor (1 lsl 6)
        ] 
        in
        print_endline (if List.exists (fun a -> a land m = a) l then "Yes" else "No")
    in
    main ()