You are given a $3\times 3$ grid. Each number in the grid is represented by $C_{ij}$ where $(i,j)$ denotes the square at the $i^{th}$ row from the top and $j^{th}$ column from the left.

Bob gets confused. According to him, 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 $a_i + b_j$. You are required to determine whether Bob is correct or not.

Input format

• The first line contains an integer $T$ denoting the number of test cases.
• Next three lines contain three space-separated integers $C_{i1}, C_{i2}$, and $C_{i3}$ denoting the $i^{th}$ row of grid $C$.

Output format

For each test case, print YES if Bob's statement is correct. Otherwise, print NO in a new line.

Constraints

$1 \le T \le 200000\\ 0 \le C_{ij} \le 1000000000$