Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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: WA: Presentation Error)

import scala.io.StdIn

object Main extends App {

  case class Dice(su1: Int, su2: Int, su3: Int, su4: Int, su5: Int, su6: Int){
    private val nums = Map(1 -> su1, 2 -> su2, 3 -> su3, 4 -> su4, 5 -> su5, 6 -> su6)
    def currentTop(): Int = nums(1)
    
    def roll(d: Char): Dice = d match {
        case 'N' => Dice(su2, su6, su3, su4, su1, su5)
        case 'S' => Dice(su5, su1, su3, su4, su6, su2)
        case 'W' => Dice(su3, su2, su6, su1, su5, su4)
        case 'E' => Dice(su4, su2, su1, su6, su5, su3)
    }
    
    def rollToNum(top: Int): Dice = {
      
      var cnt = 0
      var temp = this.copy()
      while(temp.su1 != top && cnt < 4){
        temp = temp.roll('N')
        cnt += 1
      }

      cnt = 0
      while(temp.su1 != top && cnt < 4){
        temp = temp.roll('W')
        cnt += 1
      }
      if(temp.su1 == top) temp else this
    }
    
  }
  
  val n = StdIn.readLine().toInt

  val dices = (0 until n).map { i =>
    val nums = StdIn.readLine().split(' ').map(_.toInt)
    val dice1 = Dice(nums(0), nums(1), nums(2), nums(3), nums(4), nums(5))
    // for duplicate numbers
    val numsGrouped = nums.groupBy(n => n)
    if(numsGrouped.keys.size == 2 && numsGrouped.count(p => p._2.length == 1) >= 1) {
      println()
      val t = numsGrouped.filter(p => p._2.length == 1).head
      val k = t._1
      dice1.rollToNum(k)
    } else {
      dice1
    }
  }


  var judge = false
  var i = 0
  while(!judge && i < n){
    var base = dices(i)
    var j = i+1
    while(!judge && j < n){
      var comp = dices(j)
      // search top
      var count = 0
      comp = comp.rollToNum(base.su1)
      if(base.su1 == comp.su1){
        // roll south
        base = base.roll('S')
        comp = comp.roll('S')

        count = 0
        // 2 is match / again search top, side 3 
        while(base.su1 != comp.su1 &&
          base.su3 != comp.su3 && count < 4){
          comp = comp.roll('W')
          count += 1
        }
        
        //println("base:" + base)
        //println("comp:" + comp)
        judge = base == comp
      }
      j += 1
    }
    i += 1
  }
  
  println(if(judge) "No" else "Yes")
  
}