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: Wrong Answer)

c = []
c.append(list(map(int, input().split())))
c.append(list(map(int, input().split())))
c.append(list(map(int, input().split())))

c0 = c[0][0] + c[0][1] + c[0][2]
c1 = c[1][0] + c[1][1] + c[1][2]
c2 = c[2][0] + c[2][1] + c[2][2]

# a0 + b0 = c00
# a0 + b1 = c01
# a0 + b2 = c02
# 3*a2 + b0 + b1 + b2 = c20 + c21 + c22
# 3*a2 - 3*a0 = c20 + c21 + c22 - (c00 + c01 + c02)
print(str(c))
for a0 in range(101):
    b0 = c[0][0] - a0
    b1 = c[0][1] - a0
    b2 = c[0][2] - a0
    for a1 in range(101):
        a2 = (c2 - c0 + 3 * a0) / 3
        if (
            c[1][0] - a1 == b0
            and c[1][1] - a1 == b1
            and c[1][2] - a1 == b2
            and c[2][0] - a2 == b0
            and c[2][1] - a2 == b1
            and c[2][2] - a2 == b2
        ):
            print("Yes")
            exit(0)
print("No")