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)

# ABC 088 C - Takahashi's Information
"""
高橋君の提示している条件内では、ai,biが不定でも問題ないことがポイントです。
つまり、cii = ai+biを満たせばよいので、aiをx増やしたらbiをx減らせばciiは同様に成り立ちます。
一般化すると
(𝑎1, 𝑎2, 𝑎3, 𝑏1, 𝑏2, 𝑏3) = (𝑝1, 𝑝2, 𝑝3, 𝑞1, 𝑞2, 𝑞3)から
(𝑎1, 𝑎2, 𝑎3, 𝑏1, 𝑏2, 𝑏3) = (𝑝1 + 𝑥, 𝑝2 +𝑥, 𝑝3 + 𝑥, 𝑞1 − 𝑥, 𝑞2 − 𝑥, 𝑞3 − 𝑥)にしても問題ないです。
この性質を利用して𝑎1 = 0とすると、c11=a1+b1=b1,　c12=a1+b2=b2,　c13=a1+b3=b3
が成立します。b1がわかれば上記と同様にa2,a3はわかります(c21=a2+b1,c31=a3+b1から)。
(1)a = 0として、b1,b2,b3を求める
(2)a2 = c21-b1, a3 = c31-b1からa2,a3を求める
(3)求めたa1~3とb1~3を使ってcijの我が正しいか判定する
"""
C = [list(map(int,input().split())) for __ in range(3)]

a=[0]*3
b=[0]*3
b[0],b[1],b[2]=C[0]
a[0],a[1],a[2]=0,C[1][0]-b[0],C[2][0]-b[0]
flag = True
for i in range(3):
    if flag == False:
        break
    for j in range(3):
        if C[i][j] != a[i]+b[j]:
            print("No")
            flag = False
            break
if flag == True:
    print("Yes")