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)

class Dice < Array
	def roll!(drct)
		drct.split("").each{|s|
		case s
		when "E" then
			self.replace([at(3),at(1),at(0),at(5),at(4),at(2)])
		when "N" then
			self.replace([at(1),at(5),at(2),at(3),at(0),at(4)])
		when "S" then
			self.replace([at(4),at(0),at(2),at(3),at(5),at(1)])
		when "W" then
			self.replace([at(2),at(1),at(5),at(0),at(4),at(3)])
		when "R" then
			self.replace([at(0),at(3),at(1),at(4),at(2),at(5)])
		end
		}
	end
	def is_top
		at(0)
	end
	def getr!(face)
		while at(0) != face[0] do
			roll!(["E","N","S","W"].sample)
		end
		while at(1) != face[1] do
			roll!("R")
		end
		at(2)
	end
	def is_eq(dice)
		for i in 1..4 do
			for j in 1..4 do
				return 0 if self == dice
				roll!("R")
			end
			roll!("E")
		end
		for i in 1..3 do
			roll!("N")
			for j in 1..4 do
				return 0 if self == dice
				roll!("R")
			end
		end
		return 1
	end
end

a = Array.new
b = Array.new
for i in 0..n = gets.to_i-1 do
	a[i] = Dice.new(gets.split.map(&:to_i))
end
for i in 1..n do
	b[i-1] = a[0].is_eq(a[i])
end
puts b.inject(:+) == n ? "Yes" : "No"