Reform#1911
On a picturesque plane with a Cartesian coordinate system, there existed a very traditional country from ancient times. This country had cities, numbered consecutively from to . Despite their size, these cities are considered as points on the plane due to the vastness of the plane. The coordinates of the -th city are (X_i, Y_i), and each pair of cities has unique coordinates. No cities are collinear.
Some pairs of cities are connected by bidirectional roads, each being a straight line segment between two cities. Each city has exactly roads extending from it. No road connects a city to itself, and there is at most one road between any pair of cities.
This arrangement had been unchanged for ages until a liberal king ascended to power, bringing about significant changes. A decree was issued to reform the road network, requiring:
Each city must have exactly roads extending from it.
The turning angle between the two roads from the same city must be strictly less than degrees.
No two roads should intersect anywhere other than at the cities.
The turning angle between two roads is defined as follows: if roads from city lead to cities and , the turning angle is the external angle at vertex in triangle (refer to the figure).
The task of implementing this reform was assigned to the Minister of Transport. He must decide which roads to remove and which to retain. To satisfy the king, the minister aims to choose a solution that minimizes the maximum turning angle between the two roads from any city.
The first line of the input contains an integer . Each of the following lines contains integers. The first two numbers on the -th line are X_i and Y_i. The next three numbers are the indices of the cities initially connected to the -th city by roads.
All numbers in the input are integers. 4 \leq N \leq 200, is even, -10^5 \leq X_i, Y_i \leq 10^5.
No two cities share the same coordinates. No cities are collinear.
Each city is connected by roads to exactly other cities.
There is at most one road between any pair of cities. No road connects a city to itself. Any two turning angles (not necessarily at the same city) before the reform differ by at least 10^{-5} degrees.
Any turning angle before the reform differs from degrees by at least 10^{-5} degrees.
If it is impossible to meet the king's requirements, output a single line containing Minister's life is short :(.
Otherwise, output the solution the minister should choose, as integers separated by spaces. If the -th number in the output is , it indicates that the minister should remove the road between cities and .
Beispiel 1