# Clockwise

Tags:
Time Limit:  1 s      Memory Limit:   128 MB
Submission：30     AC：21     Score：99.60

## Description

Saya have a long necklace with N beads, and she signs the beads from 1 to N. Then she fixes them to the wall to show N-1 vectors – vector i starts from bead i and end up with bead i+1.

One day, Kudo comes to Saya’s home, and she sees the beads on the wall. Kudo says it is not beautiful, and let Saya make it better.

She says: “I think it will be better if it is clockwise rotation. It means that to any vector i (i<N-1), it will have the same direction with vector i+1 after clockwise rotate T degrees, while 0T<180.”

It is hard for Saya to reset the beads’ places, so she can only remove some beads. To saving the beads, although she agrees with Kudo’s suggestion, she thinks counterclockwise rotation is also acceptable. A counterclockwise rotation means to any vector i (i<N-1), it will have the same direction with vector i+1 after counterclockwise rotate T degrees, while 0<T180.”

Saya starts to compute at least how many beads she should remove to make a clockwise rotation or a counterclockwise rotation.

Since the necklace is very-very long, can you help her to solve this problem?

## Input

The input consists of several test cases.

The first line of input in each test case contains one integer N (2<N300), which represents the number of beads.

Each of the next N lines contains two integer x and y, represents the coordinate of the beads. You can assume that 0<x, y<10000.

The last case is followed by a line containing one zero.