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 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();
			}
		}
		int[] x12 = new int[3];
		int[] x13 = new int[3];
		int[] x23 = new int[3];
		int[] y12 = new int[3];
		int[] y13 = new int[3];
		int[] y23 = new int[3];
		
		for (int i = 0; i < 3; i++) {
			x12[i] = grid[i][0] - grid[i][1];
			x13[i] = grid[i][0] - grid[i][2];
			x23[i] = grid[i][1] - grid[i][2];
			y12[i] = grid[0][i] - grid[1][i];
			y13[i] = grid[0][i] - grid[2][i];
			y23[i] = grid[1][i] - grid[2][i];
		}
		boolean flag = true;
		for (int i = 0; i < 2; i++) {
			for (int j = i + 1; j < 3; j++) {
				if (x12[i] != x12[j]) {
					flag = false;
					break;
				}
				if (x13[i] != x13[j]) {
					flag = false;
					break;
				}
				if (x23[i] != x23[j]) {
					flag = false;
					break;
				}
				if (y12[i] != y12[j]) {
					flag = false;
					break;
				}
				if (y13[i] != y13[j]) {
					flag = false;
					break;
				}
				if (y23[i] != y23[j]) {
					flag = false;
					break;
				}
			}
			if (!flag) {
				break;
			}
		}
		if (flag) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}
	}
}