B"After hearing the story of Dr. Zhang, Wowo decides to plan his own flight around the world. He already chose n checkpoints in the world map. Due to the landform and the clouds, he cannot fly too high or too low. Formally, let b_i be the height of Wowo's aircraft at checkpoint i , x_i^- <= b_i <= x_i^+ should be satisfied for all integers i between 1 and n , where x_i^- and x_i^+ are given integers. The angle of Wowo's aircraft is also limited. For example, it cannot make a 90 -degree climb. Formally, y_i^- <= b_i-b_{i-1} <= y_i^+ should be satisfied for all integers i between 2 and n , where y_i^- and y_i^+ are given integers. The final limitation is the speed of angling up or angling down. An aircraft should change its angle slowly for safety concerns. Formally, z_i^- <= (b_i - b_{i-1}) - (b_{i-1} - b_{i-2}) <= z_i^+ should be satisfied for all integers i between 3 and n , where z_i^- and z_i^+ are given integers. Taking all these into consideration, Wowo finds that the heights at checkpoints are too hard for him to choose. Please help Wowo decide whether there exists a sequence of real numbers b_1, ldots, b_n satisfying all the contraints above. Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 66 ,666 ). Description of the test cases follows. The first line of each test case contains a single integer n ( 3 <= n <= 100 ,000 ). The i -th of the next n lines contains two integers x_i^- , x_i^+ ( -10^8 <= x_i^- <= x_i^+ <= 10^8 ) denoting the lower and upper bound of b_i . The i -th of the next n-1 lines contains two integers y_{i+1}^- , y_{i+1}^+ ( -10^8 <= y_{i+1}^- <= y_{i+1}^+ <= 10^8 ) denoting the lower and upper bound of b_{i+1}-b_i . The i -th of the next n-2 lines "...