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: Time Limit Exceeded)

def c_takahashi_information(C):
    a = []
    b = []
    for a_0 in range(min(C[0]) + 1):
        for a_1 in range(min(C[1]) + 1):
            for a_2 in range(min(C[2]) + 1):
                tmp1 = [a_0, a_1, a_2]
                tmp2 = [[C[i][j] - tmp1[i]
                         for j in range(3)] for i in range(3)]
                a.append(tmp1)
                b.append(tmp2)
    for aa, bb in zip(a, b):
        for bbb in bb:
            f = True
            for i in range(3):
                for j in range(3):
                    if aa[i] + bbb[j] != C[i][j]:
                        f = False
                        break
                if not f:
                    break
            if f:
                return 'Yes'
    return 'No'
  
C = [[int(i) for i in input().split()] for j in range(3)]
print(c_takahashi_information(C))