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: Runtime Error)

import java.util.*;

public class Main {
	public static void main(String[] args) throws Exception{
	Scanner scn = new Scanner(System.in);
	int c = scn.nextInt();
      int check = 0;
      int[] a = new int[c];
      for(int i=0; i<a.length; ++i){
        a[i] = scn.nextInt();
      }
      int a1 = a[4] - a[1];
      int a2 = a[7] - a[4];
      
      if(a[5] != a[2]+a1){
        check = 1;
      }
       if(a[6] != a[3]+a1){
        check = 1;
      }
       if(a[8] != a[5]+a2){
        check = 1;
      }
       if(a[9] != a[6]+a2){
        check = 1;
      }
     
      if(check==0){
        System.out.println("Yes");
      }else{
        System.out.println("No");
      }
	}
}