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.*;
public class Main {
public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int [][] list = new int[3][3];
    int [] a_list = new int[3];
    int [] b_list = new int[3];
    int max_a = 0;
    for(int a=0;a<3;a++) {
        a_list[a] = 0;
        b_list[a] = 0;
        for (int b = 0; b < 3; b++) {
            list[a][b] = sc.nextInt();
            if(a==0&&max_a<=list[a][b]){
                max_a = list[a][b];
            }
        }
    }
    for(int a=0;a<max_a;a++){
        for(int b=0;b<3;b++){
            a_list[b]=0;
            b_list[b]=0;
        }
        a_list[0] =a;
        for(int b=0;b<3;b++){
            b_list[b]=list[0][b] - a_list[0];
            if(b_list[b]<0) break;
        }
        a_list[1] = list[1][0]-b_list[0];
        a_list[2] = list[2][0]-b_list[0];
        if(a_list[1]<0||a_list[2]<0) continue;
        for(int b=1;b<3;b++){
            if(list[b][1]!= a_list[b]+b_list[1]) break;
            if(list[b][2] != a_list[b] + b_list[2])break;
            if(b==2) a= max_a+10;
            }
            if(a==max_a+10) {
            System.out.println("Yes");
            break;
        }
        if(a==max_a-1) System.out.println("No");
    }
    }

}