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 Scala (judge verdict: Accepted)

import scala.io.Source

object Main{
  def main(args: Array[String]){
    val dices = for{
      in <- Source.stdin.getLines.toList
    } yield in

    val targets = dices.tail.map(_.split(" ").toList.map(_.toInt)).combinations(2)
    val list = for{
      target <- targets
    } yield {
      val dice1 = new Dice(target.head)
      val dice2 = new Dice(target.last)
      dice1.isEqual(dice2)
    }

    println(if(!list.foldLeft(false)((a,b) => a || b)) "Yes" else "No")
  }
}

class Dice(sur: List[Int]){
  private val index: List[Int] = sur

  def findRight(list: List[Int]): Int={
    val dice = new Dice(index)
    val kindOfDices = List[Dice](dice, dice.rotN, dice.rotS, dice.rotW, dice.rotE, dice.rotN.rotN)
    val finddice = for{
      kindOfDice <- kindOfDices
    }yield kindOfDice match{
      case x if(x.getVal(0) == list(0) && x.getVal(1) == list(1)) => x.getVal(2)
      case x if(x.rotR.getVal(0) == list(0) && x.rotR.getVal(1) == list(1)) => x.rotR.getVal(2)
      case x if(x.rotR.rotR.getVal(0) == list(0) && x.rotR.rotR.getVal(1) == list(1)) => x.rotR.rotR.getVal(2)
      case x if(x.rotR.rotR.rotR.getVal(0) == list(0) && x.rotR.rotR.rotR.getVal(1) == list(1)) => x.rotR.rotR.rotR.getVal(2)
      case _ => 0
    }

    finddice.sum
  }

  def isEqual(dice2:Dice): Boolean={
    val dice = new Dice(index)
    val kindOfDices = List[Dice](dice, dice.rotN, dice.rotS, dice.rotW, dice.rotE, dice.rotN.rotN)

    val torf = for{
      kindOfDice <- kindOfDices
    } yield kindOfDice match{
      case x if(x.index == dice2.index) => true
      case x if(x.rotR.index == dice2.index) => true
      case x if(x.rotR.rotR.index == dice2.index) => true
      case x if(x.rotR.rotR.rotR.index == dice2.index) => true
      case _ => false
    }

    def recConfirm(list: List[Boolean]): Boolean={
      if(list == Nil) false
      else list.head || recConfirm(list.tail)
    }

    recConfirm(torf)
  }

  def getVal(i: Int): Int = index(i)

  def rotR(): Dice =
    new Dice(index).rotS.rotW.rotN

  def rotN(): Dice =
    new Dice(List[Int](index(1), index(5), index(2), index(3), index(0), index(4)))

  def rotS(): Dice =
    new Dice(List[Int](index(4), index(0), index(2), index(3), index(5), index(1)))

  def rotW(): Dice =
    new Dice(List[Int](index(2), index(1), index(5), index(0), index(4), index(3)))

  def rotE(): Dice =
    new Dice(List[Int](index(3), index(1), index(0), index(5), index(4), index(2)))
}