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>

int
main(int argc, char *argv[])
{
  int c[3][3];
  for(int i = 0; i < 3; i++) scanf("%d %d %d", &c[i][0], &c[i][1], &c[i][2]);

  int a[2][3], b[3][2];

  for(int i = 0; i < 3; i++){
    for(int j = 0; j < 2; j++){
      a[j][i] = c[j + 1][i] - c[0][i];
    }
  }

  for(int i = 0; i < 2; i++){
    for(int j = 0; j < 3; j++){
      b[j][i] = c[j][i + 1] - c[j][0];
    }
  }

  int s = 0;

  for(int i = 0; i < 2; i++){
    if(a[i][0] == a[i][1] && a[i][1] == a[i][2]) s++;
  }

  for(int i = 0; i < 2; i++){
    if(b[0][i] == b[1][i] && b[1][i] == b[2][i]) s++;
  }

  if(s == 4) printf("Yes\n");
  else printf("No\n");

  return 0;
}