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 Python (3.4.3) (judge verdict: Wrong Answer)

li = []

li.append(list(map(int,input().split())))
li.append(list(map(int,input().split())))
li.append(list(map(int,input().split())))

ans = 'Yes'

a = li[0][0]
if li[0][0] == 0:
  a = 1

b = li[0][1]
if li[0][1] == 0:
  b = 1

c = li[0][2]
if li[0][2] == 0:
  c = 1

for i in range(li[0][0]):
  if li[0][0] == 0:
    i = 0
  
  for x in range(li[0][1]):
    if li[0][1] == 0:
   	  x = 0
    for y in range(li[0][2]):
      if li[0][2] == 0:
        y = 0
      
      b0 = li[0][0] - i
      b1 = li[0][1] - i
      b2 = li[0][2] - i

      if li[0][0] != i + b0:
        ans = 'No'

      if li[0][1] != x + b0:
        ans = 'No'
      
      if li[0][2] != y + b0:
        ans = 'No'

      if li[1][0] != i + b1:
        ans = 'No'

      if li[1][1] != x + b1:
        ans = 'No'
      
      if li[1][2] != y + b1:
        ans = 'No'

      if li[2][0] != i + b2:
        ans = 'No'

      if li[2][1] != x + b2:
        ans = 'No'
      
      if li[2][2] != y + b2:
        ans = 'No'

print(ans)