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( given_ary )
    @ary = given_ary
  end

  def topface( val )
    4.times do
      self.roll( "E" )
      if self.top == val
        return
      end
    end
    3.times do
      self.roll( "N" )
      if self.top == val
        return
      end
    end
  end

  def frontface( val )
    4.times do
      tmp = @ary[1]
      @ary[1] = @ary[2]
      @ary[2] = @ary[4]
      @ary[4] = @ary[3]
      @ary[3] = tmp
      if @ary[1] == val
        return
      end
    end
  end

  def roll( direction )
    case direction.downcase
    when "e"
      tmp = @ary[0]
      @ary[0] = @ary[3]
      @ary[3] = @ary[5]
      @ary[5] = @ary[2]
      @ary[2] = tmp
    when "w"
      tmp = @ary[0]
      @ary[0] = @ary[2]
      @ary[2] = @ary[5]
      @ary[5] = @ary[3]
      @ary[3] = tmp
    when "s"
      tmp = @ary[0]
      @ary[0] = @ary[4]
      @ary[4] = @ary[5]
      @ary[5] = @ary[1]
      @ary[1] = tmp
    when "n"
      tmp = @ary[0]
      @ary[0] = @ary[1]
      @ary[1] = @ary[5]
      @ary[5] = @ary[4]
      @ary[4] = tmp
    end
  end

  def top
    @ary[ 0 ]
  end

  def front
    @ary[ 5 ]
  end

  def right
    @ary[ 2 ]
  end

  def vals
    @ary
  end

  def identical( givendice )
    return @ary.zip( givendice.vals ).map{ | x, y | x - y }.inject(:+) == 0
  end

end


dice1 = Dice.new( gets.split.map(&:to_i) )
dice2 = Dice.new( gets.split.map(&:to_i) )
dice2.topface( dice1.top )
dice2.frontface( dice1.front )
puts ( dice1.identical( dice2 ) )? "Yes": "No"