B"Allen, a government secret service, has been assigned to infiltrate a mafia secret base to uncover crucial information regarding the mafia's operations. The secret base is a rectangular bounded by (x_L,y_L) , (x_L,y_R) , (x_R,y_L) , and (x_R,y_R) in a Cartesian coordinate system where x_L < x_R and y_L < y_R . There are N sensors placed inside the secret base. The i^{th} sensor is located at (x_i, y_i) and has an effective sensing radius of r_i which can detect any person who is strictly within the radius of r_i from (x_i, y_i) . In other words, the i^{th} sensor can detect a person at location (x_a, y_a) if and only if the Euclidean distance of (x_i, y_i) and (x_a, y_a) is strictly less than r_i . It is also known that the Euclidean distance of any two sensors i and j is strictly larger than r_i + r_j . Note that the Euclidean distance of two points, (x_a, y_a) and (x_b, y_b) , is sqrt{|x_a - x_b|^2 + |y_a - y_b|^2} . Allen begins his infiltration mission at location (x_s, y_s) , and his target is located at (x_t, y_t) . Allen has the power to run extremely fast in a straight line while he needs to spend extra time to change his running trajectory (to adjust his footing). Although he is a fast runner, he still needs to make sure that none of the sensors detect him while he is running, i.e. there is no point in his running trajectory which is strictly within a sensor effective sensing radius. Let P = {(x_{p_1}, y_{p_1}), ... , (x_{p_{|P|}}, y_{p_{|P|}}) } be the set of locations where Allen changes his running trajectory, thus, Allen's running trajectory with P is (x_s, y_s) rightarrow (x_{p_1}, y_{p_1}) rightarrow ... rightarrow (x_{p_{|P|}}, y_{p_{|P|}}) rightarrow (x_t, y_t) where (x_a,y_a) rightarrow (x_b,y_b) implies that Allen is running from (x_a,y_a) to (x_b,y_b) in "...