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) {
    try (Scanner sc = new Scanner(System.in)) {
      int[][] arr = new int[3][3];
      int[] a = new int[3];//𝑎1, 𝑎2, 𝑎3,
      int[] b = new int[3];//𝑏1, 𝑏2, 𝑏3
      for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
          arr[i][j] = sc.nextInt();
        }
      }

      // 1つ分かれば（ex. 𝑎1=xと仮定すると）他のa,bもxの式で表せられる
      // それで、a1=x+?=0となるxがあるとすると、a1=と仮定して他のa,bもxの式で表せられる・・・はず
      a[0] = 0;
      for (int i = 0; i < 3; i++)
        b[i] = arr[0][i] - a[0];// 𝑏𝑖 = 𝑐1,𝑖 − 𝑎1
      for (int i = 0; i < 3; i++)
        a[i] = arr[i][0] - b[0];

      boolean isGood = true;
      for (int i = 0; i < 3; i++) {
        for (int j = 0; j < 3; j++) {
          if (arr[i][j] != a[i] + b[j]) {
            isGood = false;
          }
        }
      }
      System.out.println(isGood ? "Yes" : "No");
    }

  }
}