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

\(1 \le T \le 200000\\ 0 \le C_{ij} \le 1000000000\)