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
  attr_reader :u, :f, :r, :l, :b, :d
  def initialize(line)
    @u, @f, @r, @l, @b, @d = line.split.map(&:to_i)
  end
  def rot(direc)
    case direc
    when "E";
      @u, @l, @d, @r = @l, @d, @r, @u
    when "N";
      @u, @f, @d, @b = @f, @d, @b, @u
    when "S";
      @u, @f, @d, @b = @b, @u, @f, @d
    when "W";
      @u, @l, @d, @r = @r, @u, @l, @d
    when "Z";
      @f, @r, @b, @l = @r, @b, @l, @f
    end
  end
  def dispUp
    printf "%d\n", @u
  end
  def arr
    {:u=>u, :f =>f, :r=>r, :l=>l, :b=>b, :d=>d}
  end
  def out
    return sprintf "%d %d %d %d %d %d", u, f, r, l, b, d
  end
  def diceMatch(dice2)
    dice2.arr.each{|key, val|
      if self.u == val then
        d2 = dice2.clone
        k = sprintf "%s", key
        case k
        when "d"; d2.rot("N"); d2.rot("N");
        when "f"; d2.rot("N");
        when "b"; d2.rot("S");
        when "l"; d2.rot("E");
        when "r"; d2.rot("W");
        end
        4.times do
          if self.out == d2.out then
            return "Yes"
          end
          d2.rot("Z")
        end
      end
    }
    return "No"
  end
end

n = gets.to_i
dice = Array.new(n)
i = 0
n.times{
  dice[i] = Dice.new(gets.chomp)
  i += 1
}
for i in 0..n-1
  for j in i+1..n-1
    if dice[i].diceMatch(dice[j]) == "Yes" then
      printf "No\n"
      exit
    end
  end
end
printf "Yes\n"