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 PyPy3 (7.3.0) (judge verdict: Accepted)

c = [[int(cn) for cn in input().split()] for _ in range(3)]
max_val = max(c[0])
ans = 'No'
for a1 in range(max_val + 1):
  b = [c[0][i] - a1 for i in range(3)]
  correct = True
  for i in range(2):
    ai_cand = []
    for j in range(3):
      cand = c[i + 1][j] - b[j]
      correct = cand >= 0
      if correct:
        ai_cand.append(cand)
      else:
        break
    correct = correct and (ai_cand[0] == ai_cand[1] and ai_cand[1] == ai_cand[2])
    if not correct:
      break
  if correct:
    ans = 'Yes'
    break
print(ans)