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)

(* 重複なし順列 *)
let rec perm n ls =
  if n = 0 then [[]]
  else flatmap (fun x -> List.map (fun y -> x :: y)
                                  (perm (n - 1) (remove x ls)))
               ls
and remove x ls = List.filter (fun y -> x <> y) ls
and flatten = function
  [] -> []
| x::xs -> x @ (flatten xs)
and flatmap func ls = flatten (List.map func ls)


let t = Scanf.sscanf (read_line ()) "%d %d %d" (fun a b c -> [a; b; c])
let c = Scanf.sscanf (read_line ()) "%d %d %d" (fun a b c -> [a; b; c])
let b = Scanf.sscanf (read_line ()) "%d %d %d" (fun a b c -> [a; b; c])

let bingo_list = [t; c; b; 
    [List.hd t; List.nth c 1; List.nth b 2];
    [List.nth t 2; List.nth c 1; List.hd b];

    [List.hd t; List.hd c; List.hd b];
    [List.nth t 1; List.nth c 1; List.nth b 1];
    [List.nth t 2; List.nth c 2; List.nth b 2];
    ]

let n = read_int ()

let rec read_lines_to_int_list count =
    match count with
    | 0 -> []
    | _ -> read_int () :: read_lines_to_int_list (count-1)

let value_list = read_lines_to_int_list n
let all_perms = perm 3 value_list

let rec ans lst = match lst with
     [] -> false
    | first :: rest -> if List.exists (fun x -> x = first) all_perms then true else ans rest

let () = if ans bingo_list then print_endline "Yes" else print_endline "No"