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 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

/*ソートの時に使う
int sort(const void *a, const void *b){
    return *(int*)a-*(int*)b ;
}
    qsort (data,sizeof(data),sizeof(int),sort); 
*/

int main(void){
    int c,d,e,f,g,h,i,j,k;
    scanf("%d%d%d%d%d%d%d%d%d",&c,&d,&e,&f,&g,&h,&i,&j,&k);
    
    if (c-d==f-g&&f-g==i-j){
        if (d-e==g-h&&g-h==j-k){
            if(c-f==d-g&&d-g==e-h){
                if(f-i==g-j&&g-j==h-k){
                    printf ("Yes\n");
                    exit (0);
                }
            }
        }
    }
    printf ("No\n");
	return 0 ;
}