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)

import numpy as np
from numpy.linalg import matrix_rank
A = np.array([[1,0,0,1,0,0],
            [1,0,0,0,1,0],
            [1,0,0,0,0,1],
            [0,1,0,1,0,0],
            [0,1,0,0,1,0],
            [0,1,0,0,0,1],
            [0,0,1,1,0,0],
            [0,0,1,0,1,0],
            [0,0,1,0,0,1]])

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

Ac = np.array([[1,0,0,1,0,0, c11],
            [1,0,0,0,1,0, c12],
            [1,0,0,0,0,1, c13],
            [0,1,0,1,0,0, c21],
            [0,1,0,0,1,0, c22],
            [0,1,0,0,0,1, c23],
            [0,0,1,1,0,0, c31],
            [0,0,1,0,1,0, c32],
            [0,0,1,0,0,1, c33]])

if matrix_rank(A) == matrix_rank(Ac):
    print("Yes")
else:
    print("No")