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)

# 入力を格納
C = [list(map(int, input().split())) for _ in range(3)]

# a, bをリストとして準備
a = [0] * 3
b = [0] * 3

# a1=0ならば、b1, b2, b3はC[0]に該当
b[0], b[1], b[2] = C[0][0], C[0][1], C[0][2]

# Cとbの値からa1, a2, a3の値を求める
a[0], a[1], a[2] = 0, C[1][0] - b[0], C[2][0] - b[0]

# Cとai+biを比較し、いずれかのケースで一致いない場合は出力を”No"とする
ans = "Yes"
for i in range(3):
    for j in range(3):
        if C[i][j] == (a[i] + b[j]):
            pass
        else:
            ans = "No"
            break

print(ans)