Problem:
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Dice IV

Write a program which reads $n$ dices constructed in the same way as Dice I, and determines whether they are all different. For the determination, use the same way as Dice III.

Input

In the first line, the number of dices $n$ is given. In the following $n$ lines, six integers assigned to the dice faces are given respectively in the same way as Dice III.

Output

Print "Yes" if given dices are all different, otherwise "No" in a line.

Constraints

$2 \leq n \leq 100$

$0 \leq $ the integer assigned to a face $ \leq 100$

Sample Input 1

3
1 2 3 4 5 6
6 2 4 3 5 1
6 5 4 3 2 1

Sample Output 1

No

Sample Input 2

3
1 2 3 4 5 6
6 5 4 3 2 1
5 4 3 2 1 6

Sample Output 2

Yes

Solution in Ruby (judge verdict: Accepted)

#!/usr/bin/env ruby

require 'set'

class Dice
	attr_reader :top, :s, :e

    def initialize(top, s, e, w, n, bottom)
        @top    = top
        @s      = s
        @e      = e
        @w      = w
        @n      = n
        @bottom = bottom
	end

	def rotate!(dist)
		@top, @s, @e, @w, @n, @bottom = 
		case dist
		when 'N' then [@s, @bottom, @e, @w, @top, @n]
		when 'S' then [@n, @top, @e, @w, @bottom, @s]
		when 'E' then [@w, @s, @top, @bottom, @n, @e]
		when 'W' then [@e, @s, @bottom, @top, @n, @w]
		end
	end
end

if __FILE__ == $0 then
	srand(0)

	n = gets.chomp.to_i
	dice = ([0]*n).map { |x| Dice.new(*gets.split.map(&:to_i))}
	ref  = [*1..n].map { |x| Set.new()}

	1000.times do
		if ref[0].size > 23 then
			break
		end

		dist = 'NEWS'[rand(4)]
		n.times do |i|
			ref[i].add([dice[i].top, dice[i].s, dice[i].e])
			dice[i].rotate!(dist)
		end
	end

	puts ref.to_set.size == n ? 'Yes' : 'No'
end