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: Wrong Answer)

n = gets.to_i
dices = []
n.times {dices << gets.split.map(&:to_i)}
throw = {E: [3, 2, 6, 1, 5, 4], N: [5, 1, 3, 4, 6, 2],
         S: [2, 6, 3, 4, 1, 5], W: [4, 2, 1, 6, 5, 3]}
th = {}
throw.each_key {|k| th[k] = throw[k].map(&:pred)}

rotate = ->(dir, dice) {
  next_dice = Array.new(6, 0)
  dice.each_with_index do |d, i|
    next_dice[th[dir][i]] = d
  end
  next_dice
}

adapt_same_side = ->(dice) {
  stack = [:E, :E, :E, :E, :N, :E, :E, :E, :E]
  stack.each do |dir|
    if dice[1] == dices[0][1]
      break dice
    else
      dice = rotate.(dir, dice)
    end
  end
  dice
}

is_same_dices = ->(dice1, dice2) {
  result = false
  4.times do
    if dice2 == dice1
      result = true
      break
    end
    dice2 = rotate.(:E, dice2)
  end
  result
}

new_dices = [dices[0]]
dices[1, n - 1].each {|d| new_dices << adapt_same_side.(d)}
result = "Yes"
new_dices.combination(2) do |dice1, dice2|
  if is_same_dices.(dice1, dice2)
    result = "No"
    break
  end
end
puts result