Problem:
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Dice III

Write a program which reads the two dices constructed in the same way as Dice I, and determines whether these two dices are identical. You can roll a dice in the same way as Dice I, and if all integers observed from the six directions are the same as that of another dice, these dices can be considered as identical.

Input

In the first line, six integers assigned to faces of a dice are given in ascending order of their corresponding labels.

In the second line, six integers assigned to faces of another dice are given in ascending order of their corresponding labels.

Output

Print "Yes" if two dices are identical, otherwise "No" in a line.

Constraints

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

Sample Input 1

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

Sample Output 1

Yes

Sample Input 2

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

Sample Output 2

No

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_by_ne(order_e, order_t, order_s)
    loop do
      tmp = execute_orders(["N", "S", "E", "W"].sample)
      if $east == order_e
        break
      end
    end
    3.times do
      move_north
      if $top == order_t && $south == order_s
        return true
        break
      end
    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

dice_numbers_1 = gets.chomp.split.map(&:to_i)
dice_numbers_2 = gets.chomp.split.map(&:to_i)
dice1 = Dice.new(dice_numbers_1[0], dice_numbers_1[1], dice_numbers_1[2], dice_numbers_1[3], dice_numbers_1[4], dice_numbers_1[5])
if dice1.check_dices_by_ne(dice_numbers_2[2], dice_numbers_2[0], dice_numbers_2[1])
  puts "Yes"
else
  puts "No"
end