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)


def myAnswer(C:list) -> int:
   a = [0 for _ in range(3)]
   b = [0 for _ in range(3)]
   for n,c in enumerate(C):
      a[n]=min(c)
   print(a)
   C = list(zip(*C))
   for n,c in enumerate(C):
      b[n] = min(c)
   print(b)
   C = list(zip(*C))
   for i in range(3):
      for j in range(3):
         if(C[i][j] != a[i]+b[j]):
            return "No"
   return "Yes"






def modelAnswer():
   return
def main():
   C = [list(map(int,input().split())) for _ in range(3)]
   print(myAnswer(C[:]))
   
if __name__ == '__main__':
   main()