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 JAVA (judge verdict: Accepted)

import java.io.*;
import java.util.*;


public class Main{ 

	public static void main(String args[]){
	/*	Scanner scan = new Scanner(System.in);
		Dice d01 = new Dice(scan.nextLine());
		Dice d02 = new Dice(scan.nextLine());
		if(d01.equals(d02))
			System.out.println("Yes");
		else
			System.out.println("No");*/
		
		
		Scanner scan = new Scanner(System.in);
		int dnum = scan.nextInt();
		scan.nextLine();
		HashSet<Dice> dlist = new HashSet<Dice>();
		for(int i=0; i<dnum; i++)
			if(!dlist.add(new Dice(scan.nextLine()))){
				System.out.println("No");
				return;
			}
		System.out.println("Yes");
			
	}

}
class Dice{
	int top;
	int back;
	int right;
	int left;
	int front;
	int bottom;
	public Dice(String line){
		String[] face = line.split(" ");
		top = Integer.parseInt(face[0]);
		back = Integer.parseInt(face[1]);
		right = Integer.parseInt(face[2]);		
		left = Integer.parseInt(face[3]);
		front = Integer.parseInt(face[4]);
		bottom = Integer.parseInt(face[5]);
	}
	void rotate(){
		int tmp = front;
		front = right;
		right=back;
		back = left;
		left = tmp;
	}
	public void roll(char c){
		int tmp = top;
		switch(c){
			case 'N':
				top = back;
				back=bottom;
				bottom = front;
				front = tmp;
				break;
			case 'E':
				top = left;
				left = bottom;
				bottom = right;
				right = tmp;
				break;
			case 'S':
				top = front;
				front = bottom;
				bottom = back;
				back = tmp;
				break;
			case 'W':
				top = right;
				right = bottom;
				bottom = left;
				left = tmp;
				break;
		}
	}
	boolean equalFace(Dice d){
		if(this.top == d.top && 
		   this.bottom == d.bottom &&
		   this.right == d.right &&
		   this.left == d.left &&
		   this.front == d.front &&
		   this.back == d.back)
			return true;
		else
			return false;
	}
	@Override
	public int hashCode() {
		return 0;
		/*
	    final int prime = 31;
	    int result = 1;
	    result = prime * result + top;
	    result = prime * result + bottom;
	    result = prime * result + right;
	    result = prime * result + left;
	    result = prime * result + front;
	    result = prime * result + back;
	    return result;*/
    }
	@Override
	public boolean equals(Object obj) {
		Dice d = (Dice) obj;
		return rollAllPattern(d);
	}
	public boolean rotateCheck(Dice d){
		for(int j=0;j<4;j++){
			rotate();
			if(this.equalFace(d))
				return true;
		}
		return false;
	}
	public boolean rollAllPattern(Dice d){
		for(int i=0; i<4;i++){
			roll('N');
			if(rotateCheck(d))
				return true;
		}
		roll('W');
		if(rotateCheck(d))
			return true;		
		roll('E');
		roll('E');		
		if(rotateCheck(d))
			return true;	
		return false;			
	}
	
}