The Malaysian Flight Search

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Read problems statements in Mandarin Chinese and Russian.
Problem description.
Malaysia Airlines Flight MH370 disappeared on March 8th with 239 people aboard. After a lot of theories and extensive search, the Prime Minister of Malaysia declared that the flight was crashed in the Indian Ocean.
After gathering information, the area where the Black Box is present has been identified. The Black Box has a signal transmitter which responds to a special kind of signal.
We have search planes which can go to a particular location, and send the special kind of signal in all directions to a certain range. If the Black Box receives that signal, it will respond back.
As the location of crash is very far from nearest land and the cost to operate planes are high, Officials would like to minimize the total cost of this search operation. You are to write a program to help them
For the purpose of this problem, we consider 2D coordinate system, forget about the depth of Indian Ocean and the following are true:
 We have many planes with us, each plane is defined by 3 variables (I, R, C). I is the unique id of the plane. R is the range it can transmit the special signal. C is the amount of Rupees (Yes, we are operating from India) required for one unit of travel.
 All the planes are present at (0,0).
 Same plane can be used any number of times.
 All the distances we consider in this problem are Manhattan distance. Distance between (a,b) and (c,d) is abs(ac)+abs(bd).
 Given the plane id, and coordinates (x,y) from where it has to transmit the special signal, the plane moves from (0,0) to (x,y), transmits the signal, records the reply from Black Box if any, and returns to (0,0)
 Cost of above operation would be sum of costs for (0,0) to (x,y) and (x,y) to (0,0), i.e, 2*(x+y)*C Rupees
 Black Box at position (a,b) responds to special signal from a plane at (x,y) with range r if abs(ax) + abs(by) <= r
 We always have a plane with R = 0.
 The Black Box need not be present inside the search area. It is possible that the Officials got wrong search area. Note that the Black Box can still respond to special signals.
This is an Interactive Problem, you will be given details of all available planes, and description of area inside which the Black Box is expected to be present. You need to issue commands of the form (I, x, y) which means that you would like to send plane with id I to position (x, y) and give the special signal. The automated judge will respond with "yes" or "no", "yes" if the Black Box responded, "no" otherwise.
Input
 First line of input contains n, the number of coordinate points that are present on the search area boundary.
 Following n lines contain 2D coordinates. Note that all the points on the boundary are given in the input. The boundary walls are always parallel to either of Xaxis or Yaxis.
 Next line of input contains m, the number of planes available.
 Following m lines contains 2 integers R and C. Each plane is given Id in input order starting from 0. So the first plane has Id 0, and the last plane has Id m1.
Output
 To give a command, print 3 integers I x y as defined above.
 To stop the search and report answer, print 3 integers 1 x y where (x,y) is the location of the Malaysia Airlines Flight MH370
 If the Flight is not present in the search area, print 1 1 1.
Special
Attention: the program should clear the output buffer after printing each line. It can be done using fflush(stdout) command or by setting the proper type of buffering at the beginning of the execution  setlinebuf(stdout). Failure to flush the output buffer will result in Time Limit Exceeded verdict.
For example, at C/C++ you could use the following routines:
bool SendPlane(int id, int x, int y) { printf("%d %d %d\n", id, x, y); fflush(stdout); char temp[4]; scanf("%s", temp); return temp[0]=='y'; }
Sample Input/Output
NOTE : This sample input/output does not follow constrainsin: 4 in: 1 1 in: 1 2 in: 2 2 in: 2 1 in: 2 in: 0 100 in: 1 200 out: 0 1 1 in: no out: 0 2 2 in: no out: 0 1 2 in: yes out: 1 1 2
Explanation
The search area is a square of unit lenght with bottom left corner at (1,1). The missing flight is located at (1,2). We took all the input. Then issued the plane 0 to go to (1, 1). Special judge returned "no". Finally we issued the plane 0 to go to (1, 2) and special judge gave "yes". So we found the missing flight. we then output the same by giving command "1 1 2". Score will be 2*(1+1)*100 + 2*(2+2)*100 + 2*(1+2)*100 = 1800/4 = 450.
Constraints
Search Area: 1000 ≤ n ≤ 5000
 Distance from (0,0) to any point in the search area ≤ 100000
 100000 ≤ Number of Integer Coordinate points inside the search area ≤ 200000
 You can always enclose the whole search area in a 1024*1024 square
 See test data generation for more details.
 40 ≤ m ≤ 50
 0 ≤ R ≤ 600
 100 ≤ C ≤ 10000
Test Data Generation
Search Area:
Step 1 : A square of size 1000*1000 is taken, number of points inside are 10^6.
Step 2 : A rectangle of size w*h is taken such that w and h are less than 400. Now this rectangle is placed on some random boundary point of the initial square. All the points that fall into this rectangle are removed from initial set of points.
Step 3 : Step 2 is repeated until atmost 200000 points are left. Then it is continued until a random condition fails.
Step 4 : Now we are left with at most 200000 points. This points define the search area, but in input only the points that lie on boundary are given.
Sample Graph : Click Here
Planes:
Refer constrains section for details about m, R, C. m and C are randomly chosen. Details about generation of R will not be disclosed.We always have a plane with R = 0
Missing flight:
With 0.65 probability the flight is kept inside the search area.
Position is close to boundary points and is randomly chosen with probability 1 (always) given that it is outside the search area
Scoring
For all the issued commands of the form I x y, I has to be valid id, (x,y) must be a coordinate point inside the search area (On the boundary points are also valid). Not satisfying this constrains will result in Wrong Answer.
For the command of the form 1 x y, If (x,y) is outside the search area, or there is no Flight at (x,y), it will result in Wrong Answer.
For the command of the form 1 1 1, If the fligh is actually present inside the search area, it will result in Wrong Answer.
Let Cost be the total cost of the Search operation. Now score for that test file is Cost/Number Of Coordinate points inside search area. It will show as Wrong answer if Cost is greater than 4*10^12 or number of commands issued is greater than 5*10^5.
EDITS MADEOld :It will show as Wrong answer if Cost is greater than 10^9 or number of commands issued is greater than 5*10^5.
New :It will show as Wrong answer if Cost is greater than 4*10^12 or number of commands issued is greater than 5*10^5.
Author:  anudeep2011 
Tester:  xcwgf666 
Editorial  http://discuss.codechef.com/problems/ANUMFS 
Tags  anudeep2011, challenge, interactive, may14 
Date Added:  29032014 
Time Limit:  3 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, CLOJ, FS 
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