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: Accepted)

def main():
    c11, c12, c13 = map(int, input().split())
    c21, c22, c23 = map(int, input().split())
    c31, c32, c33 = map(int, input().split())

    r1max = max([c11, c12, c13])
    r2max = max([c21, c22, c23])
    r3max = max([c31, c32, c33])
    c1max = max([c11, c21, c31])
    c2max = max([c12, c22, c32])
    c3max = max([c13, c23, c33])
    for a1 in range(0, r1max + 1):
        for a2 in range(0, r2max + 1):
            for a3 in range(0, r3max + 1):
                m = max([a1, a2, a3])
                for b1 in range(0, c1max - m + 1):
                    if a1 + b1 == c11 and a2 + b1 == c21 and a3 + b1 == c31:
                        for b2 in range(0, c2max - m + 1):
                            if a1 + b2 == c12 and a2 + b2 == c22 and a3 + b2 == c32:
                                for b3 in range(0, c3max - m + 1):
                                    if a1 + b3 == c13 and a2 + b3 == c23 and a3 + b3 == c33:
                                        print('Yes')
                                        return

    print('No')
    return


if __name__ == '__main__':
    main()