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 C (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
int main(void){
    // Your code here!
    int c[3][3];
    
    for(int i = 0; i < 3; i++){
        for(int j = 0; j < 3; j++){
            scanf("%d",&c[i][j]);
        }
    }
    
    for(int a1 = 0; a1 <= 100; a1++){
        int b1,b2,b3;
        b1 = c[0][0] -a1;
        b2 = c[0][1] -a1;
        b3 = c[0][2] -a1;
        
        if(b1 < 0 || b2 < 0 || b3 < 0){
            break;
        }
        
        for(int a2 = 0; a2 <= 100; a2++){
            for(int a3 = 0; a3 <= 100; a3++){
                int flag = 1;
                int a[3];
                a[1] = a2;
                a[2] = a3;
                int b[3];
                b[0] = b1;
                b[1] = b2;
                b[2] = b3;
                for(int i = 1; i < 3; i++){
                    for(int j = 0; j < 3; j++){
                        if(c[i][j] - b[j] != a[i]){
                            flag = 0;
                        }
                    }
                }
                
                if(flag == 1){
                    printf("Yes\n");
                    return 0;
                }
            }
        }
    }
    
    printf("No\n");
}