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) {
        // write your code here
        Scanner sc = new Scanner(System.in);

        int leftTop = sc.nextInt();
        int middleTop = sc.nextInt();
        int rightTop = sc.nextInt();
        int leftMiddle = sc.nextInt();
        int middleMiddle = sc.nextInt();
        int rightMiddle = sc.nextInt();
        int leftDown = sc.nextInt();
        int middleDown = sc.nextInt();
        int rightDown = sc.nextInt();

        String ans = "Yes";
        int[] aTop = {0, leftTop - middleTop, leftTop - rightTop};
        int[] aMiddle = {0, leftMiddle - middleMiddle, leftMiddle - rightMiddle};
        int[] aDown = {0, leftDown - middleDown, leftDown - rightDown};

        int[] bLeft = {0, leftTop - leftMiddle, leftTop - leftDown};
        int[] bMiddle = {0, middleTop - middleMiddle, middleTop - middleDown};
        int[] bRight = {0, rightTop - rightMiddle, rightTop - rightDown};

        if (!Arrays.equals(aTop, aMiddle) || !Arrays.equals(aTop, aDown)) {
            ans = "No";
        }

        if (!Arrays.equals(bLeft, bMiddle) || !Arrays.equals(bLeft, bRight)) {
            ans = "No";
        }

        System.out.println(ans);
    }
}