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)

open Batteries
open BatPrintf

let dbg n = Printf.eprintf "%s\n" @@ dump n; n

let scan fmt f =
  Scanf.sscanf (read_line ()) fmt f

let scan_list cnv =
  read_line ()
  |> String.split_on_char ' '
  |> List.map cnv

let scan_listn n cnv =
  List.range 1 `To n |> List.map (fun _ -> cnv @@ read_line ())

let bsearch_ge arr a =
  let l = Array.length arr in
  match Array.bsearch Int.ord arr a with
  | `All_lower -> l
  | `All_bigger -> 0
  | `Just_after n -> l - n -1
  | `At n -> l - n
  | `Empty -> 0

let rec zip xs ys =
  match xs, ys with
  | [], _ -> []
  | _, [] -> []
  | x::xs, y::ys ->
    (x, y) :: zip xs ys

let square x = x * x

let as_ = scan_listn 3
    (fun s -> String.split_on_char ' ' s |> List.Labels.map ~f:Int.of_string)
let n = scan "%d" identity
let bs = scan_listn n Int.of_string
let bingo = [[(0,0);(0,1);(0,2)]; [(1,0); (1,1); (1,2)]; [(2,0);(2,1);(2,2)];
             [(0,0);(1,0);(2,0)]; [(0,1); (1,1); (2,1)]; [(0,2);(1,2);(2,2)];
             [(0,0);(1,1);(2,2)];
             [(2,0);(1,1);(0,2)]]
let () =
  List.mapi
    (fun i a -> List.mapi (fun j b -> if List.exists ((=) b) bs then Some (i,j) else None) a) as_
  |> List.flatten
  |> List.filter Option.is_some
  |> List.map Option.get
  |> (fun l -> List.exists ((=) true) @@ List.map (fun b -> (List.fold_left (fun r c -> List.exists ((=) c) l && r) true b)) bingo)
  |> (fun ans -> printf "%s\n" (if ans then "Yes" else "No"))