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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Data.Bool
import Data.List
import Data.Maybe
import Data.Vector.Generic ((!))
import qualified Data.Vector as V
import qualified Data.Vector.Mutable as VM

main = interact $ sub . lines

sub (l1:l2:l3:ls) = sol v bs
  where
  v = V.fromListN 3 $ V.fromListN 3 . fmap (read::String->Int) . words <$> [l1,l2,l3]
  bs = fmap read $ tail ls :: [Int]

sol v bs = bool "No" "Yes" . bingo $ V.map (\u -> foldl' mark u bs) v

bingo v = V.any (V.all (==0)) v
  || any (\j -> V.all (\u -> u!j==0) v) [0..2]
  || all (\i -> v!i!i==0) [0..2]
  || all (\i -> v!i!(2-i)==0) [0..2]

mark u b = maybe u (\i -> V.modify (\w -> VM.write w i 0) u) $ V.findIndex (==b) u