408. Game with points
Time limit per test: 0.25
second(s)
Memory limit: 65536
kilobytes
input: standard
output: standard
Recently Petya has discovered new game with points. Rules of the game are quite simple. First, there is only
one point
A_{0} with coordinates (0, 0). Then Petya have to draw
N another points. Points must be drawn
consequently and each new point must be connected with exactly one of the previous points by a segment.
Let's decribe the game process more formally. At the
ith step Petya chooses the position of the point
A_{i} (not
necessarily with integer coordinates). Than he chooses one of the previously drawn points in order to connect it with the
point
A_{i}. Lets call this point
B. The following conditions must be held:
Point A_{i} must not coincide with any of the previous points.
Point A_{i} must not lie on the previously drawn segments.
Segment A_{i}B must not have common points with previously drawn segments, except possibly the point B.
Segment A_{i}B must not cover any of the previous points, except the point B.
Length of the segment A_{i}B must not exceed 1.
After drawing each point Petya computes two values.
The largest number of segments which share a common point.
The largest euclid distance between some pair of points.
After each step Petya gains the score which is equal to the product of these values.
Find out which is the maximal score Petya can gain after the whole game.
Input
Input contains single integer number N (0 ≤ N ≤ 1000).
Output
Output the maximal score that Petya can gain. Your answer must be accurate up to 10^{3}.
Example(s)
sample input

sample output

2

5.000

sample input

sample output

4

20.000
