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.*;
public class Main {
	public static void main(String[] args)  {
		Scanner scan = new Scanner(System.in);
		int[][] c = new int [3][3];
		for (int i = 0;i < 3; ++i){
			for (int k = 0;k < 3; ++k){
				c[i][k] = Integer.parseInt(scan.next());
			}
		}

		int[] x = new int [3];
		int[] y = new int [3];
		x[0] = 0;

		for (int i = 0;i < 3; ++i){
			y[i] = c[0][i]-x[0];
		}

		for (int i = 0;i < 3; ++i){
			x[i] = c[i][0]-y[0];
		}
		boolean ok = true;
		for (int i = 0;i < 3; ++i){
			for (int k = 0;k < 3; ++k){
				if (c[i][k] != x[i]+y[k]){
					ok = false;
				}
			}
		}

		System.out.print(ok?"Yes":"No");
	}
}

//end