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
	TOP=0
	FRONT=1
	RIGHT=2
	LEFT=3
	BACK=4
	BOTTOM=5
	
	def initialize( nums )
		@face = nums
	end
	
	def rolltoTopIndex( faceindex )
		case faceindex
		when FRONT
			roll( "N" )
		when RIGHT
			roll( "W" )
		when LEFT
			roll( "E" )
		when BACK
			roll( "S" )
		when BOTTOM
			roll( "NN" )
		when TOP
		end
	end
	
	def roll( actions )
		for i in ( 0 ... actions.length )
			t = 0
			case actions[i]
			when "E"
				t =   @face[ TOP  ]
				@face[ TOP  ] =   @face[ LEFT  ]
				@face[ LEFT  ] =   @face[ BOTTOM  ]
				@face[ BOTTOM  ] =   @face[ RIGHT  ]
				@face[ RIGHT  ] = t
			when "N"
				t =   @face[ TOP  ]
				@face[ TOP  ] =   @face[ FRONT  ]
				@face[ FRONT  ] =   @face[ BOTTOM  ]
				@face[ BOTTOM  ] =   @face[ BACK  ]
				@face[ BACK  ] = t
			when "S"
				t =  @face[ TOP  ]
				@face[ TOP  ] =  @face[ BACK  ]
				@face[ BACK  ] =  @face[ BOTTOM  ]
				@face[ BOTTOM  ] =  @face[ FRONT  ]
				@face[ FRONT  ] = t	
			when "W"
				t =  @face[ TOP  ]
				@face[ TOP  ] =  @face[ RIGHT  ]
				@face[ RIGHT  ] =  @face[ BOTTOM  ]
				@face[ BOTTOM  ] =  @face[ LEFT  ]
				@face[ LEFT  ] = t	
			when "M"
				t =  @face[ FRONT  ]
				@face[ FRONT  ] =  @face[ RIGHT  ]
				@face[ RIGHT  ] =  @face[ BACK  ]
				@face[ BACK  ] =  @face[ LEFT  ]
				@face[ LEFT  ] = t				
			end
		end
	end
	attr_accessor :face
end

diceface = gets.split( " " ).map { |val| val.to_i }
dice1 = Dice.new( diceface )
diceface = gets.split( " " ).map { |val| val.to_i }
dice2 = Dice.new( diceface )

cnt = 0
catch ( :samedice ) do
	for i in ( Dice::TOP ... Dice::BOTTOM )
		if dice1.face[Dice::TOP] == dice2.face[i]
			dice2.rolltoTopIndex( i )
			for j in ( Dice::FRONT .. Dice::BACK )
				if dice1.face[Dice::FRONT] == dice2.face[Dice::FRONT]
					cnt = 0
					for k in ( Dice::TOP ... Dice::BOTTOM )
						if dice1.face[k] == dice2.face[k]
							cnt += 1
						end
					end
					throw :samedice if cnt == 6
				end
				dice2.roll( "M" )
			end
		end
		dice2.face = diceface
	end
end

if cnt == 6
	puts( "Yes" )
else
	puts( "No" )
end