Problem:
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Dice III

Write a program which reads the two dices constructed in the same way as Dice I, and determines whether these two dices are identical. You can roll a dice in the same way as Dice I, and if all integers observed from the six directions are the same as that of another dice, these dices can be considered as identical.

Input

In the first line, six integers assigned to faces of a dice are given in ascending order of their corresponding labels.

In the second line, six integers assigned to faces of another dice are given in ascending order of their corresponding labels.

Output

Print "Yes" if two dices are identical, otherwise "No" in a line.

Constraints

$0 \leq $ the integer assigned to a face $ \leq 100$

Sample Input 1

1 2 3 4 5 6
6 2 4 3 5 1

Sample Output 1

Yes

Sample Input 2

1 2 3 4 5 6
6 5 4 3 2 1

Sample Output 2

No

Solution in Scala (judge verdict: Accepted)

import scala.io.StdIn._
import scala.annotation.tailrec

object Main {

  trait Monoid[A]{
    def op(a1: A, a2: A): A
    def zero: A
  }

  type Per = List[Int]
  type Rot = Dice => Dice

  object DiceRoll extends Monoid[Rot]{

    def op(rot1: Rot, rot2: Rot): Rot = (dice: Dice) => rot2(rot1(dice))
    def zero: Rot = (dice: Dice)=>dice

    val north = List(2,6,3,4,1,5).map(_ - 1)
    val east = List(4,2,1,6,5,3).map(_ - 1)
    val ccw = List(1,4,2,5,3,6).map(_ - 1)

    def rot(perm: Per): Rot = (dice: Dice) => Dice(perm.map(dice.pip))

    def axial(f: Rot): List[Rot] = List(zero,f,op(f,f),op(op(f,f),f))

    def enumerateTop(f: Rot = zero, n: Int = 6): List[Rot] = {
      if(n<=0)List[Rot]()
      else if(n%2==0) f :: enumerateTop(op(f,rot(north)),n-1)
      else f :: enumerateTop(op(f,rot(east)),n-1)
    }

    def enumerate: List[Rot] = enumerateTop().flatMap( e => axial(rot(ccw)).map(op(e,_)))
  }

  case class Dice(pip: List[Int])

  def main(args: Array[String]): Unit = {
    val pip1 = readLine.split(" ").map(_.toInt).toList
    val pip2 = readLine.split(" ").map(_.toInt).toList
    val all1: List[Dice] = DiceRoll.enumerate.map(_(Dice(pip1)))
    println(if(all1.exists(_.pip.corresponds(pip2)(_ == _))) "Yes" else "No")
  }
}