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: Accepted)

import java.util.*;

class Main{
	
	public static void main(String[] args){
		
		Scanner sc = new Scanner(System.in);
		
		int C[][] = new int[3][3];
		
		int sum = 0;
		
		for(int i = 0 ; i < 3 ; i ++){
			for(int j = 0 ; j < 3 ; j ++){
				C[i][j] = sc.nextInt();
				sum = sum + C[i][j] ;
			}
		}
		
		boolean result = false;
		
//		System.out.println(sum);
		
		if(sum % 3 == 0){
			
			int D = sum / 3;
			if(D == C[0][0] + C[1][1] + C[2][2] &&
			   D == C[0][1] + C[1][2] + C[2][0] &&
			   D == C[0][2] + C[1][0] + C[2][1] &&
			   D == C[0][2] + C[1][1] + C[2][0] &&
			   D == C[0][1] + C[1][0] + C[2][2] &&
			   D == C[0][0] + C[1][2] + C[2][1] ){
			   	result = true;
			   }
		}
		
		System.out.println( result ? "Yes" : "No");
	}
}