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)

n = [[0 for i in range(3)] for j in range(3)]

for i in range(3):
  x,y,z = input().split()
  n[i][0] = int(x)
  n[i][1] = int(y)
  n[i][2] = int(z)
  
a = [0,0,0]
b = [0,0,0]

isCmp = False

for j in range(100 +1):
  b[0] = j
  
  a[0] = n[0][0] -b[0]
  a[1] = n[1][0] -b[0]
  a[2] = n[2][0] -b[0]
  b[1] = n[0][1] -a[0]
  b[2] = n[0][2] -a[0]
  
  if  n[0][0] == a[0]+b[0] \
  and n[1][1] == a[1]+b[1] \
  and n[2][2] == a[2]+b[2]:
    print('Yes')
    isCmp = True
    break

    
if isCmp == False:
  print('No')