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: Runtime Error)

let check_bingo board hits =
  (* ビンゴ対象となる配列のインデックス *)
  let check_list = [[0;1;2]; [3;4;5]; [6;7;8]; [0;3;6]; [1;4;7]; [2;5;8]; [0;4;8]; [2;4;6]] in
  (* インデックスを値に変換 *)
  let rec get_cell board l cell_values =
    match l with
    | [] -> cell_values
    | x::xs ->
       get_cell board xs ((Array.get board x)::cell_values)
  in
  (* ある列/行/斜めがビンゴかチェック *)
  let is_bingo l hits = List.for_all (fun x -> (List.mem x hits)) l in
  let rec check_bingo_sub board l =
    match l with
    | [] -> "No"
    | x::xs ->
       let check_cell_list = get_cell board x [] in
       let result = is_bingo check_cell_list hits in
       if result then "Yes" else check_bingo_sub board xs
  in
  check_bingo_sub board check_list

(* 盤面入力 *)
let rec input_boards n board =
  match n with
  | 0 -> Array.of_list (List.rev board)
  | m ->
     let new_board = Scanf.scanf "%d %d %d\n" (fun a b c -> c :: b :: a :: board) in
     input_boards (m-1) new_board

(* 当たりの入力 *)
let rec input_hits n hits =
  match n with
  | 0 -> hits
  | m ->
     let input = read_int () in
     input_hits (m-1) (input::hits)

let _ =
  let board = input_boards 3 [] in
  let n_hit = read_int () in
  let hits  = input_hits n_hit [] in
  let ans = check_bingo board hits in
  print_endline ans