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: Accepted)

class Dice
  def initialize(numbers)
    @numbers = numbers
    @map = {:top => 1, :R => 6, :S => 2, :E => 3, :N => 5, :W => 4}
  end
 
  def move(vec)
    case vec
    when "N"
      temp = @map.clone
      temp[:top] = @map[:S]
      temp[:R] = @map[:N]
      temp[:S] = @map[:R]
      temp[:N] = @map[:top]
      @map = temp.clone
    when "W"
      temp = @map.clone
      temp[:top] = @map[:E]
      temp[:R] = @map[:W]
      temp[:E] = @map[:R]
      temp[:W] = @map[:top]
      @map = temp.clone
    when "S"
      temp = @map.clone
      temp[:top] = @map[:N]
      temp[:R] = @map[:S]
      temp[:S] = @map[:top]
      temp[:N] = @map[:R]
      @map = temp.clone
    when "E"
      temp = @map.clone
      temp[:top] = @map[:W]
      temp[:R] = @map[:E]
      temp[:E] = @map[:top]
      temp[:W] = @map[:R]
      @map = temp.clone
    end
  end
 
  def spin
    temp = @map.clone
    temp[:E] = @map[:N]
    temp[:W] = @map[:S]
    temp[:S] = @map[:E]
    temp[:N] = @map[:W]
    @map = temp.clone
  end
 
  def top_number
    @numbers[@map[:top] - 1]
  end
 
  def right_number
    @numbers[@map[:E] - 1]
  end
 
  def front_number
    @numbers[@map[:S] - 1]
  end
 
  def back_number
    @numbers[@map[:N] - 1]
  end
 
  def left_number
    @numbers[@map[:W] - 1]
  end
 
  def bottom_number
    @numbers[@map[:R] - 1]
  end
 
  def get_place(number)
    index = @numbers.index(number)
    @map.key(index + 1)
  end
 
  def numbers
    @numbers
  end
 
  def map
    @map
  end
 
  def equal?(dice)
    count = 1
    while count <= 6 do
      if dice.top_number == self.top_number
        4.times do
          if dice.left_number == self.left_number &&
             dice.right_number == self.right_number &&
             dice.front_number == self.front_number &&
             dice.back_number == self.back_number &&
             dice.bottom_number == self.bottom_number then
             return true
          end
          dice.spin
        end
      end
      if count % 2 == 0
        dice.move("N")
      else
        dice.move("W")
      end
      count += 1
    end
    return false
  end
end
 
dice1 = Dice.new(gets.split.map(&:to_i))
dice2 = Dice.new(gets.split.map(&:to_i))
 
if dice1.equal?(dice2)
  puts "Yes"
else
  puts "No"
end