Byteland Tours

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Read problems statements in Mandarin Chinese and Russian.
As part of a new program to attract tourists to Byteland, Chef has been placed in charge of organizing a series of bus tours around the city. There are N scenic locations (points on the plane) in Byteland (numbered 0 through N1), and M bidirectional scenic roads, each of which connects two scenic locations via a straight line. Chef wishes to organize the tours according to the following rules:
 A tour is defined as sequence of locations, where a tour bus begins at the first location, and moves directly from each location to the next location in the sequence until it reaches the last location. There must be a scenic road between consecutive locations.
 A tour does not have to start and end at the same location, but it is allowed.
 A tour cannot visit the same location more than once, with the possible exception of the start/end location.
 A tour cannot cross itself. That is, none of the roads belonging to a tour may intersect.
 Each road must be visited by exactly one tour.
Setting up tours is expensive, so Chef wishes to minimize the total number of tours. Optimal solutions are not required, but solutions that use fewer tours will score more points (see the scoring section below). However, your solution must use at most (N+M)/2 tours or else it will be judged Wrong Answer.
Input
Input will begin with a line containing an integer N. Following this will be N lines containing the locations of the N scenic locations. Each location is given as a pair of integers, with the ith line giving x_i and y_i, the respective x and y coordinates of the ith scenic location. Following this will be N lines containing N characters each. The ith character of the jth line will be 'Y' if there is a scenic road connecting locations i and j, and 'N' otherwise.
Output
First, print an integer K, the number of tours. Then print K tour descriptions. Each tour description should consist of an integer L, the length of the tour (in roads), followed by L+1 integers, the ordinal numbers of the locations on the tour, in order.
Scoring
Your score is K*N/M. Lower scores will earn more points.
We have 50 official test files. You must correctly solve all test files to receive OK. During the contest, your overall score is the sum of the scores on the first 10 test files. After the contest, all solutions will be rescored by the sum of the scores on the rest 40 test files. Note, that public part of the tests can not contain some border cases.
Constraints
 20 ≤ N ≤ 50
 0 ≤ x_i, y_i ≤ 100
 No three points will be collinear.
 The ith character of the ith row of the road descriptions will be 'N'.
 The ith character of the jth row of the road descriptions will equal the jth character of the ith row.
 Each city will be connected to at least one road.
Sample Input
6 2 3 10 0 10 7 3 7 9 8 2 1 NNNYNY NNYYNN NYNYYN YYYNYN NNYYNY YNNNYN
Sample Output
3 4 3 0 5 4 2 1 4 3 3 1 2 3 1
This sample output would score 3*6/8 = 2.25 points.
Test Case Generation
N will be chosen randomly and uniformly between 20 and 50, inclusive. Each point's coordinates are chosen randomly and uniformly between 0 and 100, inclusive. If two points coincide or three points are collinear, the process is restarted (with the same value of N).
A real value P is chosen randomly and uniformly between 0.3 and 1.0. Between each pair of cities a road exists with probability P. If some city has no roads, the process is restarted (with the same value of P).
Author:  pieguy 
Tester:  white_king 
Editorial  http://discuss.codechef.com/problems/TOURBUS 
Tags  challenge, dynamicprogramming, greedy, heuristic, jan14, pieguy, search 
Date Added:  28112013 
Time Limit:  1 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, PYP3, CLOJ, FS 
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