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 Java (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            int[][] C = new int[3][3];
            for (int r = 0; r < 3; r++) {
                for (int c = 0; c < 3; c++) {
                    C[r][c] = in.nextInt();
                }
            }

            int[] a = new int[3];
            int[] b = new int[3];
            int[][] a2 = new int[3][3];
            a[0] = 0;

            for (int c = 0; c < 3; c++) {
                b[c] = C[0][c] - a[0];
            }

            for (int r = 0; r < 3; r++) {
                for (int c = 0; c < 3; c++) {
                    a2[r][c] = C[r][c] - b[c];
                }
            }

            for (int r = 0; r < 3; r++) {
                for (int c = 1; c < 3; c++) {
                    if (a2[r][c - 1] != a2[r][c]) {
                        System.out.println("No");
                        return;
                    }
                }
            }
            System.out.println("Yes");
        }
    }
}