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: Accepted)

import java.util.*; 

class Main{
public static void main(String[] args){
	Scanner sc=new Scanner(System.in);

  		int[][] ci=new int[3][3];
		for(int c=0;c<3;c++){
    		ci[c][0]=sc.nextInt();
          	ci[c][1]=sc.nextInt();
         	ci[c][2]=sc.nextInt();
    	}
    int count=0;
  	for(int b=0;b<2;b++){
     if((ci[b+1][0]-ci[b][0])!=(ci[b+1][1]-ci[b][1])||(ci[b+1][1]-ci[b][1])!=(ci[b+1][2]-ci[b][2])){
     	count=1;
     }
    }
    for(int b=0;b<2;b++){
     if((ci[0][b+1]-ci[0][b])!=(ci[1][b+1]-ci[1][b])||(ci[1][b+1]-ci[1][b])!=(ci[2][b+1]-ci[2][b])){
     	count=1;
     }
    }
 	if(count==0){
    		System.out.println("Yes");
    	}else{
     		System.out.println("No");
   	 }


    }
}