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.