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
  attr_accessor :faces

  # |T F L|
  # |B U R|
  def initialize(faces)
    top, front, right, left, back, bottom = faces
    @faces = [[top, bottom], [front, back], [left, right]]
  end

  def move(commands)
    commands.split('').each do |com|
      case com.upcase.to_sym
      when :E
        faces[0], faces[2] = faces[2], faces[0].reverse
      when :W
        faces[0], faces[2] = faces[2].reverse, faces[0]
      when :N
        faces[0], faces[1] = faces[1], faces[0].reverse
      when :S
        faces[0], faces[1] = faces[1].reverse, faces[0]
      end
    end
  end

  def method_missing(face)
    if %i(top bottom front back left right).include? face
      {
        top:    faces[0][0],
        bottom: faces[0][1],
        front:  faces[1][0],
        back:   faces[1][1],
        left:   faces[2][0],
        right:  faces[2][1]
      }[face]
    else
      super
    end
  end

  def ==(other)
    commands = (["N"]*3 + ["E"]*3)
    0.upto(commands.size) do |r|
      commands.permutation(r).each do |c|
        move(c.join)
        return true if faces == other.faces
      end
    end
    false
  end

  def clone
    self.class.new([top, front, right, left, back, bottom])
  end

  def info
    p({ T: top, F: front, R: right, L: left, U: back, B: bottom })
  end

end

$stdin = DATA if $<.eof?

dice_a = Dice.new(gets.split)
dice_b = Dice.new(gets.split)

puts(dice_a == dice_b ? "Yes" : "No")

__END__
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