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: Wrong Answer)

cs = [list(map(int,input().split()))
     for _ in range(3)]

tr = []
for c in zip(*cs):
    tr.append(list(c))

def transpose(cs):
    tr = []
    for c in zip(*cs):
        tr.append(list(c))
    return tr

def diff_equal(cs):
    kl = []
    lm = []
    for c in cs:
        k,l,m = c
        kl.append(k-l)
        lm.append(l-m)
#     print(kl)
#     print(lm)
    if len(set(kl)) != 1:
        return False
    if len(set(lm)) != 1:
        return False

def check():
    if not diff_equal(cs):
        return False
    if not diff_equal(transpose(cs)):
        return False
    return True

def main():
    if check():
        print("Yes")
    else:
        print("No")

main()