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 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])
    for a1 in range(0, r1max + 1):
        r2max = max([c21, c22, c23])
        for a2 in range(0, r2max + 1):
            r3max = max([c31, c32, c33])
            for a3 in range(0, r3max + 1):
                m = max([a1, a2, a3])
                for b1 in range(0, 101 - m):
                    C11 = a1 + b1
                    C21 = a2 + b1
                    C31 = a3 + b1
                    if C11 == c11 and C21 == c21 and C31 == c31:
                        for b2 in range(0, 101 - m):
                            C12 = a1 + b2
                            C22 = a2 + b2
                            C32 = a3 + b2
                            if C12 == c12 and C22 == c22 and C32 == c32:
                                for b3 in range(0, 101 - m):
                                    C13 = a1 + b3
                                    C23 = a2 + b3
                                    C33 = a3 + b3
                                    if C13 == c13 and C23 == c23 and C33 == c33:
                                        print('Yes')
                                        return

    print('No')
    return


if __name__ == '__main__':
    main()