/*
	Infasuratoarea convexa
	calc unghi: atan(y/x) * 180 / PI;
*/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define PI 3.14159265

struct punct
{
	float x,y;
	bool verificat;
};
punct V[10]; int maxPuncte=0;
punct INF[10]; int maxInf=0;

void adauga_punct(punct *vector, int &maxElem,float x,float y);
bool citeste_fisier(char *nume_fisier);
void gaseste_infasuratoare();
punct *gaseste_cel_mai_din_stanga();
punct *gaseste_urmatorul_punct(punct *PCurent, int &zonaC);
bool update_punct_curent_unghi(punct *curent,punct *ptest,punct *&dest, float &unghi, int zona, bool &first);
bool verif_update(punct *sursa,punct *&dest,float &unghi1,float unghi2, int zona,bool &first);

void scrie_fisier(char *nume_fisier);

int main()
{
	if ( citeste_fisier("infasuratoare.in") == 0 )
		return 0;
	gaseste_infasuratoare();
	scrie_fisier("infasuratoare.out");
	//system("PAUSE");
	return 0;
}

void gaseste_infasuratoare()
{
	punct *curent=gaseste_cel_mai_din_stanga();
	punct *first= curent;
	int zona = 0;
	do
	{
		curent = gaseste_urmatorul_punct(curent,zona);
		adauga_punct(INF,maxInf,curent->x,curent->y);
		curent->verificat = 1;
	}
	while ( curent != first );

}

punct *gaseste_urmatorul_punct(punct *PCurent, int &zonaC)
{
	int i;
	punct *Next=0;
	float unghi=0;
	bool first=true;
	int zonac = 5;
	for(i=0;i<maxPuncte;i++)
	{
		if ( &V[i] == PCurent )
			continue;
		if ( V[i].verificat == false )
		{
			if ( V[i].x >= PCurent->x )
			{
				if ( (V[i].y > PCurent->y) && ( zonaC <= 1 ))   // zona 1
				{
					if ( zonac > 1 )
						first = true;
					if ( update_punct_curent_unghi(PCurent,&V[i],Next,unghi,1,first) )
						zonac = 1;
				}
				else if ( ( zonac > 1 ) && ( zonaC <= 2) )    // zona 2
				{
					if ( zonac > 2 )
						first = true;
					if (update_punct_curent_unghi(PCurent,&V[i],Next,unghi,2,first))
						zonac = 2;
				}
			}
			else if ( zonac > 2 )
			{
				if ( ( V[i].y < PCurent->y) && ( zonaC <= 3 ) )   // zona 3
				{
					if ( zonac > 3 )
						first = true;
					if (update_punct_curent_unghi(PCurent,&V[i],Next,unghi,3,first))
						zonac = 3;
				}
				else if ( (zonac > 3) && ( zonaC <= 4) )   // zona 4
				{
					if (update_punct_curent_unghi(PCurent,&V[i],Next,unghi,4,first))
						zonac = 4;
				}
			}
		}
	}
	zonaC = zonac;
	return Next;
}

bool update_punct_curent_unghi(punct *curent,punct *ptest,punct *&dest, float &unghi, int zona,bool &first)   // zona 1 = dreapta sus, 2 = dreapta jos, 3 = stanga jos, 4 = stanga sus
{
	float unghitmp=0;
	float x,y;
	if ( zona == 1 )
	{
		x = abs(ptest->x-curent->x);
		y = abs(ptest->y-curent->y);
		unghitmp = ( atan(y/x )* 180 / PI );
		
		return verif_update(ptest,dest,unghi,unghitmp,1,first);
	}
	if ( zona == 2 )
	{
		x = abs(ptest->x-curent->x);
		y = abs(curent->y-ptest->y);
		unghitmp = ( atan(y/x )* 180 / PI );
		
		return verif_update(ptest,dest,unghi,unghitmp,2,first);
	}
	if ( zona == 3 )
	{
		x = abs(curent->x-ptest->x);
		y = abs(curent->y-ptest->y);
		unghitmp = ( atan(y/x )* 180 / PI );
		
		return verif_update(ptest,dest,unghi,unghitmp,3,first);
	}
	if ( zona == 4 )
	{
		x = abs(ptest->x-curent->x);
		y = abs(ptest->y-curent->y);
		unghitmp = ( atan(y/x )* 180 / PI );
		
		return verif_update(ptest,dest,unghi,unghitmp,4,first);
	}
}

bool verif_update(punct *sursa,punct *&dest,float &unghi1,float unghi2, int zona,bool &first)
{
	if ( first || ( zona == 1 && (unghi1 < unghi2)) )
	{
		dest = sursa;
		unghi1 = unghi2;
		first = false;
		return 1;
	}
	if ( first || ( zona == 2 && (unghi1 > unghi2) ) )
	{
		dest = sursa;
		unghi1 = unghi2;
		first = false;
		return 1;
	}
	if ( first || ( zona == 3 && (unghi1 < unghi2) ) )
	{
		dest = sursa;
		unghi1 = unghi2;
		first = false;
		return 1;
	}
	if ( first || ( zona == 4 && ( unghi1 > unghi2 ) ) )
	{
		dest = sursa;
		unghi1 = unghi2;
		first = false;
		return 1;
	}
	return 0;
}

punct *gaseste_cel_mai_din_stanga()
{
	punct *stg = &V[0];
	for(int i=1;i<maxPuncte;i++)
		if ( stg->x > V[i].x )
			stg = &V[i];
	return stg;
}

void scrie_fisier(char *nume_fisier)
{
	FILE *f = fopen(nume_fisier,"w");
	if ( f == 0 )
		return;
	fprintf(f,"%d\n",maxInf);
	for(int i=0;i<maxInf;i++)
		fprintf(f,"%f %f\n",INF[i].x,INF[i].y);

	fclose(f);
}

bool citeste_fisier(char *nume_fisier)
{
	FILE *f = fopen(nume_fisier,"r");
	if ( f == 0 )
		return 0;
	float x,y;
	int maxP=0;
	fscanf(f,"%d",&maxP);
	if ( maxP == 0 )
	{
		fclose(f);
		return 0;
	}
	for(int i=0;i<maxP;i++)
	{
		fscanf(f,"%f %f",&x,&y);
		adauga_punct(V,maxPuncte,x,y);
	}
	fclose(f);
	return 1;
}

void adauga_punct(punct *vector, int &maxElem,float x,float y)
{
	vector[maxElem].x = x;
	vector[maxElem].y = y;
	vector[maxElem].verificat = false;
	maxElem++;
}