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[][] c = new int[3][3];

        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                c[i][j] = sc.nextInt();
            }
        }

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

        for (int i = 0; i <= 100; i++) {
            for (int j = 0; j <= 100; j++) {
                for (int k = 0; k <= 100; k++) {
                    a[0] = i;
                    a[1] = j;
                    a[2] = k;

                    b[0] = c[0][0] - i;
                    b[1] = c[0][1] - i;
                    b[2] = c[0][2] - i;

                    if (check(a, b, c)) {
                        System.out.println("Yes");
                        return;
                    }
                }
            }
        }
        System.out.println("No");
    }

    static boolean check(int a[], int b[], int c[][]) {
        for (int i = 0; i < 3; i++) {
            for (int j = 0; j < 3; j++) {
                if (a[i] + b [j] != c[i][j]) {
                    return false;
                }
            }
        }
        return true;
    }
}