Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 Matrix < Array
  attr_reader :n, :m
  def initialize(arr, row = false, cul = false)
    if (row and cul) or !(Array === arr[0])
      arr.flatten!
      super()
      for i in 0...row ||= arr.length
        self << [*arr[i * cul, cul]]
      end
      @n, @m = row, cul
    elsif Array === arr[0]
      super(arr)
      @n, @m = arr.length, arr[0].length
    else
      raise
    end
  end
  
  def self.e(row = 0)
    result = []
    for i in 0...row
      result << (0...row).map{|num|num == i ? 1: 0}
    end
    return Matrix.new(result)
  end
  
  def *(other)
    if Matrix === other
      return mmul(other)
    elsif Numeric === other
      return self.map{|item|item.map{|i|i * other}}
    end
  end
  
  def dup
    return Matrix.new(self.map(&:dup), @n, @m)
  end
  
  def **(num)
    if num == 0
      return 1
    else
      result = Matrix.e(@n)
      num.to_s(2).each_char{|c|result = result * result * self ** (c.to_i)}
      return result
    end
  end
  
  def to_s
    result = []
    for i in 0...@n
      result << self[i].join(" ")
    end
    return result
  end
  
  def to_ary
    self
  end
  
  private
  def mmul(other)
    result = []
    for i in 0... self.n
      for j in 0... other.m
        temp = 0
        for k in 0... self.m
          temp += self[i][k] * other[k][j]
        end
        result << temp
      end
    end
    return Matrix.new(result, self.n, other.m)
  end
end
class Dice
  attr_reader :att, :num
  def initialize(i, ii, iii, iv, v, vi, ichi = [0, 1, 0], ni = [0, 0, 1], san = [1, 0, 0], posx = 0, posy = 0)
    @att = Matrix.new([ichi, ni, san], 3, 3)
    @num = Array.new([nil, i, ii, iii, iv, v, vi])
    @x, @y = posx, posy
  end
  
  def ==(other)
    if (self.num && other.num) == other.num
      if (other.num.index(self.num[1]) + other.num.index(self.num[6]) == 7) and (other.num.index(self.num[2]) + other.num.index(self.num[5]) == 7)
        return ((@num[3] == other.set(@num[1], @num[2]).getx) and (@num[3] == other.set(@num[6], @num[5]).getx))
      else
        return false
      end
    else
      return false
    end
  end
  
  def dup
    return Dice.new(*@num[1..6].dup, *@att.dup, @x, @y)
  end
  
  def set(top, front)
    return self.dup.set!(top, front)
  end
  
  def set!(top, front)
    while top != gety or front != getz
     while top != gety and front != getz
       rotx!
     end
     while top == gety and front != getz
       roty!
     end
     while top != gety and front == getz
       rotz!
     end
    end
    return self
  end
  
  def getx(i = 1)
    return @num[i * (@att.index{|item|item[0] != 0} + 1) * @att.find{|item|item[0] != 0}[0]]
  end
  
  def gety(i = 1)
    return @num[i * (@att.index{|item|item[1] != 0} + 1) * @att.find{|item|item[1] != 0}[1]]
  end
  
  def getz(i = 1)
    return @num[i * (@att.index{|item|item[2] != 0} + 1) * @att.find{|item|item[2] != 0}[2]]
  end
  
  def rotx(i = 1)
    return self.dup.rotx!(i)
  end
  
  def roty(i = 1)
    return self.dup.roty!(i)
  end
  
  def rotz(i = 1)
    return self.dup.rotz!(i)
  end
  
  def rotx!(i = 1)
    @att *= Matrix.new([[1, 0, 0], [0, 0, -i], [0, i, 0]], 3, 3)
    return self
  end
  
  def roty!(i = 1)
    @att *= Matrix.new([[0, 0, i], [0, 1, 0], [-i, 0, 0]], 3, 3)
    return self
  end
  
  def rotz!(i = 1)
    @att *= Matrix.new([[0, -i, 0], [i, 0, 0], [0, 0, 1]], 3, 3)
    return self
  end
end
if Dice.new(*gets.split(" ").map(&:to_i)) == Dice.new(*gets.split(" ").map(&:to_i))
  puts "Yes"
else
  puts "No"
end