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 C# (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Math;

class program{
    public static void Main(){
        var nums1 = Console.ReadLine().Split(' ').Select(_ => int.Parse(_)).ToList();
        var dice1 = new Dice(nums1);
        var nums2 = Console.ReadLine().Split(' ').Select(_ => int.Parse(_)).ToList();
        var dice2 = new Dice(nums2);

        if(Dice.SameDice(dice1,dice2)){
            Console.WriteLine("Yes");
        }else{
            Console.WriteLine("No");
        }
    }
}

class Dice{
    public List<Face> faces = new List<Face>(6);

    public Dice(List<int> nums){
        faces.Add(new Face(nums[0],'T'));
        faces.Add(new Face(nums[1],'S'));
        faces.Add(new Face(nums[2],'E'));
        faces.Add(new Face(nums[3],'W'));
        faces.Add(new Face(nums[4],'N'));
        faces.Add(new Face(nums[5],'B'));
    }

    public void Rotate(char dir){
        if(dir == 'N'){
            var tmpnum = getFace('T').num;
            getFace('T').num = getFace('S').num;
            getFace('S').num = getFace('B').num;
            getFace('B').num = getFace('N').num;
            getFace('N').num = tmpnum;
        }
        if(dir == 'W'){
            var tmpnum = getFace('T').num;
            getFace('T').num = getFace('E').num;
            getFace('E').num = getFace('B').num;
            getFace('B').num = getFace('W').num;
            getFace('W').num = tmpnum;
        }
        if(dir == 'S'){
            var tmpnum = getFace('T').num;
            getFace('T').num = getFace('N').num;
            getFace('N').num = getFace('B').num;
            getFace('B').num = getFace('S').num;
            getFace('S').num = tmpnum;
        }
        if(dir == 'E'){
            var tmpnum = getFace('T').num;
            getFace('T').num = getFace('W').num;
            getFace('W').num = getFace('B').num;
            getFace('B').num = getFace('E').num;
            getFace('E').num = tmpnum;
        }
    }

    public int getRightNum(int top, int south){
        var s = faces.First(_ => _.num == south);

        if(s.dir == 'N'){
            Rotate('N');
            Rotate('N');
        }
        if(s.dir == 'T'){
            Rotate('S');
        }
        if(s.dir == 'E'){
            Rotate('W');
            Rotate('S');
        }
        if(s.dir == 'W'){
            Rotate('E');
            Rotate('S');
        }
        if(s.dir == 'B'){
            Rotate('N');
        }

        var t = faces.First(_ => _.num == top);

        if(t.dir == 'W'){
            Rotate('E');
        }
        if(t.dir == 'B'){
            Rotate('E');
            Rotate('E');
        }
        if(t.dir == 'E'){
            Rotate('W');
        }

        return getFace('E').num;
    }

    public Face getFace(char d){
        return faces.First(_ => _.dir == d);
    }

    public static bool SameDice(Dice dice1, Dice dice2){
        //sをあわせる
        var s = dice2.faces.First(_ => _.num == dice1.getFace('S').num);

        if(s.dir == 'N'){
            dice2.Rotate('N');
            dice2.Rotate('N');
        }
        if(s.dir == 'T'){
            dice2.Rotate('S');
        }
        if(s.dir == 'E'){
            dice2.Rotate('W');
            dice2.Rotate('S');
        }
        if(s.dir == 'W'){
            dice2.Rotate('E');
            dice2.Rotate('S');
        }
        if(s.dir == 'B'){
            dice2.Rotate('N');
        }

        //tをあわせる
        var t = dice2.faces.First(_ => _.num == dice1.getFace('T').num);
        if(t.dir == 'N') return false;

        if(t.dir == 'W'){
            dice2.Rotate('E');
        }
        if(t.dir == 'B'){
            dice2.Rotate('E');
            dice2.Rotate('E');
        }
        if(t.dir == 'E'){
            dice2.Rotate('W');
        }

        if(Dice.compFacenum(dice1,dice2,'E') && Dice.compFacenum(dice1,dice2,'W') && Dice.compFacenum(dice1,dice2,'N') && Dice.compFacenum(dice1,dice2,'B')){
            return true;
        }else{
            return false;
        }
    }

    public static bool compFacenum(Dice dice1, Dice dice2, char dir){
        var f1 = dice1.getFace(dir);
        var f2 = dice2.getFace(dir);
        return f1.num == f2.num;
    }
}

class Face{
    public int num;
    public char dir;

    public Face(int n, char d){
        num = n;
        dir = d;
    }
}