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: Wrong Answer)

#include <stdio.h>
#include <stdbool.h>

int main(void)
{

  int c[9];

  for (int i = 0; i < 9; i++) {
    scanf("%d", &c[i]);
  }

  int min = 11;
  for (int i = 0; i < 3; i++) {
    if (min > c[i]) {
      min = c[i];
    }
    
  }

  int b[3];

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

  int min2=10;
  int min3=10;

  for (int i = 0; i < 3; i++) {
    if (min2 > c[3+i]) {
      min2 = c[i+3];
    }
    if (min3 > c[6+i]) {
      min3 = c[i+6];
    }
  }
  for (int i = 0; i < 3; i++) {
  }

  bool flag = true;

  for (int i = 0; i < 3; i++) {
    if (c[3+i] - min2 != b[i] ) {
       flag = false;
    }
    if (c[6+i] - min3 != b[i] ) {
       flag = false;
    }

  }
  

  if (flag == true) {
    printf("Yes\n");
  } else {
    printf("No\n");
  }
  return 0;
}