I. Mission Possibletime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAllen, 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}), \dots, (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 \dots \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 a straight line. The set P is feasible if and only if with P, Allen is not detected by any sensor and is not running out of the secret base (although, Allen is allowed to run along the secret base perimeter). Note that x_p and y_p, (x_p,y_p) \in P, are not necessarily integers; they can be real numbers.Your task in this problem is to find any one feasible P which contains no more than 1000 points.InputInput begins with a line containing five integers: N x_L y_L x_R y_R (0 \le N \le 50; 0 \le x_L < x_R \le 1000; 0 \le y_L < y_R \le 1000) representing the number of sensors and the secret base (x_L, y_L, x_R, y_R), respectively. The next line contains two integers: x_s y_s (x_L < x_s < x_R; y_L < y_s < y_R) representing Allen's initial location. The next line contains two integers: x_t y_t (x_L < x_t < x_R; y_L < y_t < y_R) representing Allen's target location. It is guaranteed that x_s \ne x_t or y_s \ne y_t. The next N lines each contains three integers: x_i y_i r_i (x_L < x_i - r_i < x_i + r_i < x_R; y_L < y_i - r_i < y_i + r_i < y_R; 1 \le r_i \le 1000) representing a sensor at location (x_i, y_i) with an effective sensing radius of r_i. It is guaranteed that the Euclidean distance of any two sensors i and j is larger than r_i + r_j. It is also guaranteed that the Euclidean distance of (x_s,y_s) and (x_t,y_t) to any sensor i is larger than r_i.OutputOutput in a line an integer representing the size of a feasible P. The next |P| lines each contains two real numbers (separated by a single space); the j^{th} line contains x_j y_j representing the j^{th} point in P. You may output any feasible P with no more than 1000 points.Due to the nature of the output (floating point), let us define an epsilon \epsilon to be 10^{-6} to verify the output. Consider Q_1 = (x_s, y_s), Q_{j+1} = P_j for all 1 \le j \le |P|, and Q_{|P|+2} = (x_t, y_t). Then, P is considered correct if and only if P contains no more than 1000 points and all of the following are satisfied:   x_L - \epsilon \le x_{p_k} \le x_R + \epsilon and y_L - \epsilon \le y_{p_k} \le y_R + \epsilon for all 1 \le k \le |P| (Allen is not running out of the secret base).  For all 1 \le k < |Q|, let S_k be the line segment connecting Q_k and Q_{k+1} (Allen is running in straight line). For all 1 \le i \le N, let (x_{k,i},y_{k,i}) be the point along S_k that is the closest to the i^{th} sensor's location, (x_i,y_i). Let d_{k,i} be the Euclidean distance between (x_{k,i},y_{k,i}) and (x_i,y_i). Then, the constraint r_i \le d_{k,i} + \epsilon should be satisfied (Allen is not detected by any sensor).  All points in Q are distinct. Two points, (x_a,y_a) and (x_b,y_b), are considered distinct if and only if |x_a - x_b| > \epsilon or |y_a - y_b| > \epsilon. ExamplesInput
3 2 2 50 26
4 14
48 14
15 13 7
36 16 6
46 18 3
Output
2
13.25 23.1234567
36.591003 7.1
Input
1 0 0 1000 1000
100 501
900 501
500 251 250
Output
0
NoteExplanation for the sample input/output #1The figure above shows the P from the sample output. Note that there exists a feasible P with only one point in this sample, although you are not required to find such P.
3 2 2 50 26
4 14
48 14
15 13 7
36 16 6
46 18 3

2 13.25 23.1234567 36.591003 7.1 
['*3000']