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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>

struct M
{
  int value[9];
  int operator()(int i, int j)
  {
    return value[(i % 3) * 3 + (j % 3)];
  }
};

int main()
{
  M m;
  for (int i = 0; i < 9; ++i)
  {
    scanf("%d", m.value + i);
  }

  for (int i = 0; i < 3; ++i)
  {
    for (int j = 0; j < 3; ++j)
    {
      if
      (
        m(i, j) - m(i + 1, j) != m(i, j + 1) - m(i + 1, j + 1) ||
        m(i, j) - m(i, j + 1) != m(i + 1, j) - m(i + 1, j + 1)
      )
      {
        puts("No");
        return 0;
      }
    }
  }
  puts("Yes");
  return 0;
}