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 Control.Applicative
import Control.Monad
import Data.List
import Data.Bool (bool)
import Data.Vector (Vector, (!), (//))
import qualified Data.Vector as V

main :: IO ()
main = do
  xs <- f
  ys <- f
  zs <- f
  n <- readLn
  solve (V.fromList (xs ++ ys ++ zs)) <$> replicateM n readLn >>= putStrLn
  where
    f = map read <$> words <$> getLine

solve :: Vector Int -> [Int] -> String
solve v xs = bool "No" "Yes" $ vv ! 0 == 0 && vv ! 1 == 0 && vv ! 2 == 0 ||
                               vv ! 3 == 0 && vv ! 4 == 0 && vv ! 5 == 0 ||
                               vv ! 6 == 0 && vv ! 7 == 0 && vv ! 8 == 0 ||
                               vv ! 0 == 0 && vv ! 3 == 0 && vv ! 6 == 0 ||
                               vv ! 1 == 0 && vv ! 4 == 0 && vv ! 7 == 0 ||
                               vv ! 2 == 0 && vv ! 5 == 0 && vv ! 8 == 0 ||
                               vv ! 0 == 0 && vv ! 4 == 0 && vv ! 8 == 0 ||
                               vv ! 2 == 0 && vv ! 4 == 0 && vv ! 6 == 0
  where
    vv = foldl' f v xs
    f t x = case V.findIndex (== x) t of
             Just i -> t // [(i, 0)]
             Nothing -> t