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: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main{
  public static void main(String[] args){
    Scanner scan = new Scanner(System.in);
    int[][] c = new int[3][3];
    int[] r = new int[3];
    int a = 101;
    boolean flag = true;

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

    outside:for(int i = 0; i < 3; i++){
      for(int j = 0; j < 3; j++){
        a = Math.min(c[i][j], a);
      }
      if(i == 0){
        for(int j = 0; j < 3; j++){
          r[j] = c[i][j] - a;
        }
      }
      if(i > 0){
        for(int j = 0; j < 3; j++){
          if(r[j] != c[i][j]-a){
            flag = false;
            System.out.println("No");
            break outside;
          }
        }
      }
    }

    if(flag == true){System.out.println("Yes");}
  }
}