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 PyPy3 (2.4.0) (judge verdict: Accepted)

from sys import stdin


if __name__ == "__main__":
    _in = [_.rstrip() for _ in stdin.readlines()]
    c_arr = []
    for i in range(3):
        _ = list(map(int,_in[i].split(' ')))
        c_arr.append(_)
    # vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv
    sum_c_arr = sum([sum(c) for c in c_arr])
    if (c_arr[0][0]+c_arr[1][1]+c_arr[2][2]) == sum_c_arr/3 and \
       (c_arr[1][0]+c_arr[2][1]+c_arr[0][2]) == sum_c_arr/3 and \
       (c_arr[0][1]+c_arr[1][2]+c_arr[2][0]) == sum_c_arr/3 and \
       (c_arr[2][0]+c_arr[1][1]+c_arr[0][2]) == sum_c_arr/3 and \
       (c_arr[1][0]+c_arr[0][1]+c_arr[2][2]) == sum_c_arr/3 and \
       (c_arr[0][0]+c_arr[2][1]+c_arr[1][2]) == sum_c_arr/3:
        TF = 'Yes'
    else:
        TF = 'No'
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
    print(TF)