AT_abc467_d [ABC467D] Concentric Circles

Do there exist two circles $ C_1 $ and $ C_2 $ on the $ xy $ -plane satisfying all of the following conditions? Here, $ C_1 $ and $ C_2 $ may coincide. - The two distinct points $ (P_x, P_y) $ and $ (Q_x, Q_y) $ lie on the circumference of $ C_1 $ . - The two distinct points $ (R_x, R_y) $ and $ (S_x, S_y) $ lie on the circumference of $ C_2 $ . - $ C_1 $ and $ C_2 $ have the same center. You are given $ T $ test cases; solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case $ \mathrm{case}_t $ is given in the following format: > $ P_x $ $ P_y $ $ Q_x $ $ Q_y $ $ R_x $ $ R_y $ $ S_x $ $ S_y $

Output $ T $ lines. The $ t $ -th line should contain the answer to the $ t $ -th test case. For each test case, output `Yes` if there exist two circles $ C_1 $ and $ C_2 $ satisfying all of the conditions, and `No` otherwise.

### Sample Explanation 1 Consider the first test case. As shown in the figure below, if we let $ C_1 $ be the circle with center $ (1,0) $ and radius $ 1 $ , and $ C_2 $ be the circle with center $ (1,0) $ and radius $ 2 $ , the conditions are satisfied. For the second test case, letting both $ C_1 $ and $ C_2 $ be the circle with center $ (0,0) $ and radius $ 1 $ satisfies the conditions.  ### Constraints - $ 1 \leq T \leq 5 \times 10^4 $ - $ -10^9 \leq P_x,P_y,Q_x,Q_y,R_x,R_y,S_x,S_y \leq 10^9 $ - $ (P_x, P_y) \neq (Q_x, Q_y) $ - $ (R_x, R_y) \neq (S_x, S_y) $ - All input values are integers.