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
  #   1
  # 4 2 3 5
  #   6
  attr_reader :pips
  def initialize(*pips)
    @pips = pips
  end

  def rotate!(direction)
    pips = case direction
    when :n then [2, 6, 3, 4, 1, 5].map { |i| i - 1 }
    when :e then [4, 2, 1, 6, 5, 3].map { |i| i - 1 }
    when :w then [3, 2, 6, 1, 5, 4].map { |i| i - 1 }
    when :s then [5, 1, 3, 4, 6, 2].map { |i| i - 1 }
    when :z then [1, 3, 5, 2, 4, 6].map { |i| i - 1 }
    end
    @pips = @pips.values_at(*pips)
    self
  end

  def rotate_to_top!(pip)
    case @pips.index(pip) + 1
    when 1 then self
    when 2 then self.rotate!(:n)
    when 3 then self.rotate!(:w)
    when 4 then self.rotate!(:e)
    when 5 then self.rotate!(:s)
    when 6 then self.rotate!(:n).rotate!(:n)
    end
  end
end

dice1 = Dice.new(*gets.split.map(&:to_i))
dice2 = Dice.new(*gets.split.map(&:to_i))

dice2.rotate_to_top!(dice1.pips[0])
3.times do
  break if dice2.pips[1] == dice1.pips[1]
  dice2.rotate!(:z)
end

puts dice1.pips == dice2.pips ? 'Yes' : 'No'