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
  V={N:0,E:1,S:2,W:3}
  def initialize(label)
    @label=label # Top down Rignt Left up Bottom
    @top=1
    @around=[5,3,2,4] # U R D L
    # 右に転がす場合
    # 対角値(レフト,idx3)が上面(top)になる
    # 右(idx1)にもともと上面だった値（top）が入る
    # その対角面(右,idx1)には対角値（合計7になる値）が入る
    # 1 => [5,3,2,4]
    # 4 => [5,1,2,6]
    # 下に転がす場合
    # 1 => [5,3,2,4]
    # 5 => [6,3,1,4]
  end
  def set_position(top_value,front_value)
    set_uniq_top(top_value)
    set_front(front_value)
  end
  def set_uniq_top(top_value)
    # 与えられた値（ラベル値）になるようにダイスを回転させる
    # 縦横の回転数を計算して実際に動かす
    top_num=@label.index(top_value)+1
    # TOP面をあわせる
    if top_num==@top then
    elsif idx=@around.index(top_num)
      rn=self.reverse_vector(idx)
      v=V.key(rn)
      self.move(v)
    elsif
      2.times{self.move("S")}
    end
  end
  def set_front(front_value)
    # 与えられた値（ラベル値）になるようにダイスを回転させる
    # 縦横の回転数を計算して実際に動かす
    front_num=@label.index(front_value)+1
    # FRONT面を合わせる
    if idx=@around.index(front_num)
      n=reverse_vector(idx)
      self.turn(n) unless n==0
    else
      puts "i can not"
    end
  end
  def turn(n)
    # n回右に回転する（TOPは変わらず）
    # n = turn_right * n
    @around.push(@around.shift(n)).flatten!
  end
  def move(v)
    # v = U,R,D,L
    #     N,E,S,W
    #     0,1,2,3
    vn=V[v.to_sym] # 移動方向のインデックス数値
    rn=reverse_vector(vn) # 対角のインデックス数値（2を足す。4を超えていた場合は剰余）
    @top,@around[vn]=@around[rn],@top
    @around[rn]=7-@around[vn]
  end
  def state
    arr=[]
    arr<<@label[@top-1]
    @around.each do |n|
      arr<<@label[n-1]
    end
    return arr
  end
  def reverse_vector(vn)
    return (vn+2)%4
  end
end

def uniq_value(label)
  label.each do |i|
    return i if label.count{|j|i==j} == 1
  end
  puts "uniq none"
end
def code_run3
  label1=$stdin.gets.split.map(&:to_i)
  d1=Dice.new(label1)
  label2=$stdin.gets.split.map(&:to_i)
  d2=Dice.new(label2)

  t=uniq_value(label1)
  d1.set_uniq_top(t)
  f=d1.state[3] #down(front)
  d2.set_position(t,f)
  p [ t,f ]
  puts d1.state==d2.state ? "Yes" : "No"
end


  code_run3