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 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
      	int i,j;
        int c[][] = new int[3][3];
      	int check = 0;
        int a[] = new int[3];
        int b[] = new int[3];      
        for(i = 0;i<3;i++){
         for(j=0;j<3;j++){
           c[i][j] = sc.nextInt();
         }
        }
      
        if(c[0][0] == 0){
          a[0] = 0;
          b[0] = c[0][0];
          b[1] = c[0][1];
          b[2] = c[0][2];
          a[1] = c[1][0] - b[0];
          a[2] = c[2][0] - b[0];
          if(a[0]+b[0] == c[0][0] && a[1]+b[1] == c[1][1] && a[2]+b[2] == c[2][2]){
             System.out.println("Yes"); 
             System.exit(0);
          }   
        }else{
		  for(i = 1;i <= c[0][0]; i++){
            a[0] = i;
            b[0] = c[0][0] - i;
            b[1] = c[0][1] - i;
            b[2] = c[0][2] - i;
            a[1] = c[1][0] - b[0];
            a[2] = c[2][0] - b[0];
            
          	if(a[0]+b[0] == c[0][0] && a[1]+b[1] == c[1][1] && a[2]+b[2] == c[2][2]){
              if(a[1] >=0 && a[2] >=0 && b[1] >= 0 && b[2] >= 0){
                System.out.println("Yes"); 
                System.exit(0);
              }
            }
          }
        }
        System.out.println("No"); 
    }
}