Score: 300 points
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.
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}
If Takahashi's statement is correct, print Yes
; otherwise, print No
.
1 0 1 2 1 2 1 0 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.
2 2 2 2 1 2 2 2 2
No
Takahashi is incorrect in this case.
0 8 8 0 8 8 0 8 8
Yes
1 8 6 2 9 7 0 7 7
No