Problem:
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Dice IV

Write a program which reads $n$ dices constructed in the same way as Dice I, and determines whether they are all different. For the determination, use the same way as Dice III.

Input

In the first line, the number of dices $n$ is given. In the following $n$ lines, six integers assigned to the dice faces are given respectively in the same way as Dice III.

Output

Print "Yes" if given dices are all different, otherwise "No" in a line.

Constraints

$2 \leq n \leq 100$

$0 \leq $ the integer assigned to a face $ \leq 100$

Sample Input 1

3
1 2 3 4 5 6
6 2 4 3 5 1
6 5 4 3 2 1

Sample Output 1

No

Sample Input 2

3
1 2 3 4 5 6
6 5 4 3 2 1
5 4 3 2 1 6

Sample Output 2

Yes

Solution in Ruby (judge verdict: Wrong Answer)

class Dice
  def initialize(t, s, e, w, n, b)
    $north = n
    $south = s
    $east = e
    $west = w
    $top = t
    $bottom = b
  end

  def execute_orders(orders)
    length = orders.length
    for i in 0...length
      if orders[i] == "N"
        move_north
      elsif orders[i] == "S"
        move_south
      elsif orders[i] == "E"
        move_east
      elsif orders[i] == "W"
        move_west
      else
        puts "error!"
      end
    end
  end

  def check_dices_same(order_t, order_s, order_e, order_w, order_n, order_b)
      100.times do
        execute_orders(["N", "W"].sample)
        return true if $top == order_t && $south == order_s && $east == order_e && $west == order_w && $north == order_n && $bottom == order_b
      end
    return false
  end


  private
  def move_north
    north = $north
    south = $south
    top = $top
    bottom = $bottom
    $north = top
    $top = south
    $bottom = north
    $south = bottom
  end

  def move_south
    north = $north
    south = $south
    top = $top
    bottom = $bottom
    $south = top
    $bottom = south
    $north = bottom
    $top = north
  end

  def move_east
    top = $top
    bottom = $bottom
    east = $east
    west = $west
    $east = top
    $bottom = east
    $west = bottom
    $top = west
  end

  def move_west
    top = $top
    bottom = $bottom
    east = $east
    west = $west
    $west = top
    $bottom = west
    $east = bottom
    $top = east
  end
end

n = gets.chomp.to_i
dices = []
n.times do
  dice = gets.chomp.split.map(&:to_i)
  dices << dice
end
flag = 0
for i in 0...n-1
  dice = Dice.new(dices[i][0], dices[i][1], dices[i][2], dices[i][3], dices[i][4], dices[i][5])
  for j in i+1...n
    if dice.check_dices_same(dices[j][0], dices[j][1], dices[j][2], dices[j][3], dices[j][4], dices[j][5])
      puts "No"
      flag += 1
      break
    end
  end
  # if flag == 1
  #   break
  # end
  # if dice.check_dices_same(dices[n-1][0], dices[n-1][1], dices[n-1][2], dices[n-1][3], dices[n-1][4], dices[n-1][5])
  #   puts "No"
  #   flag += 1
  #   break
  # end
end
if flag == 0
  puts "Yes"
end