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.Scanner;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int[][] grid = new int[3][3];
		for(int i =0; i < 3;i++){
			for(int j =0;j<3;j++){
				grid[i][j] = sc.nextInt();
			}
		}
		boolean b = true;
		for(int i =0; i < 3; i++){
			int x = 0;
			int y = 0;
			for(int j =0;j<3;j++){
				int bX = grid[j][i] - grid[j][((i+1) % 3)];
				int bY = grid[i][j] - grid[((i+1) % 3)][j];
				if(j ==0){
					x = bX;
					y = bY;
				}else{
					b &= x == bX;
					b &= y == bY;
				}
				if(!b) break;
			}
			if(!b) break;
		}
		System.out.println(b ? "Yes" : "No");
	}
}