Problem:
Score: 300 points

Problem Statement

We have a 3 \times 3 grid. A number c_{i, j} is written in the square (i, j), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

According to Takahashi, there are six integers a_1, a_2, a_3, b_1, b_2, b_3 whose values are fixed, and the number written in the square (i, j) is equal to a_i + b_j.

Determine if he is correct.

Constraints

c_{i, j} \ (1 \leq i \leq 3, 1 \leq j \leq 3) is an integer between 0 and 100 (inclusive).

Input

Input is given from Standard Input in the following format:

c_{1,1} c_{1,2} c_{1,3}
c_{2,1} c_{2,2} c_{2,3}
c_{3,1} c_{3,2} c_{3,3}

Output

If Takahashi's statement is correct, print Yes; otherwise, print No.

Sample Input 1

1 0 1
2 1 2
1 0 1

Sample Output 1

Yes

Takahashi is correct, since there are possible sets of integers such as: a_1=0,a_2=1,a_3=0,b_1=1,b_2=0,b_3=1.

Sample Input 2

2 2 2
2 1 2
2 2 2

Sample Output 2

No

Takahashi is incorrect in this case.

Sample Input 3

0 8 8
0 8 8
0 8 8

Sample Output 3

Yes

Sample Input 4

1 8 6
2 9 7
0 7 7

Sample Output 4

No

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;

class Main{

	public static void main(String[] args) {




		Scanner scan = new Scanner(System.in);
		//		int N = scan.nextInt();
		//		int K = scan.nextInt();

		int data[] = new int[10];
		int x=0;
		for(int i = 1;i < 10;i++){
			data[i] = scan.nextInt();
		}
		int  a= 0;
		int  b= 0;
		int  c= 0;
		int  d= 0;
		int  e= 0;
		int  f= 0;

		for(;a < 101;a++){
			for(;b < 101;b++){

				for(;c < 101;c++){
					for(;d < 101;d++){
						if(data[1] == a + d &&data[4] == b + d &&data[7] == c + d){

							for(;e < 101;e++){
								if(data[2] == a + e  && data[5] == b + e && data[8] == c + e ){

									for(;f < 101;f++){
										if(  data[3] == a + f 
												&& data[6] ==b  + f
												&& data[9] == c + f) {
											System.out.println("Yes");
											x ++;

										}
									}
								}

							}
						}

					}

				}
				
			}
			








		}
		if(x == 0){
			System.out.println("No");
		}




	}
}