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 LuaJIT (2.0.4) (judge verdict: Accepted)

function mark(a_rev, b)
  local marked = {false, false, false,
                  false, false, false,
                  false, false, false}
  for i = 1, #b do
    local bi = b[i]
    if a_rev[bi] then
      marked[a_rev[bi]] = true
    end
  end
  return marked
end

function bingo(marked)
  local bingos = {
    {1, 4, 7}, {2, 5, 8}, {3, 6, 9},
    {1, 2, 3}, {4, 5, 6}, {7, 8, 9},
    {1, 5, 9}, {3, 5, 7}
  }

  for i = 1, 8 do
    local c = bingos[i]
    if marked[c[1]] and marked[c[2]] and marked[c[3]] then
      return true
    end
  end

  return false
end

local a_rev = {}
for i = 1, 9 do
  a = io.read("*n")
  a_rev[a] = i
end

local n = io.read("*n")

local b = {}
for i = 1, n do
  b[i] = io.read("*n")
end

local marked = mark(a_rev, b)
if bingo(marked) then
  print("Yes")
else
  print("No")
end