struct xy{
int x;
int y;
xy(){
}
xy(int m){
x=m;
y=m;
}
xy(int x,int y){
this->x=x;
this->y=y;
}
xy operator *(xy&m){return xy(x *m.x,y *m.y);}
xy operator /(xy&m){return xy(x /m.x,y /m.y);}
xy operator %(xy&m){return xy(x %m.x,y %m.y);}
xy operator +(xy&m){return xy(x +m.x,y +m.y);}
xy operator -(xy&m){return xy(x -m.x,y -m.y);}
xy operator <<(xy&m){return xy(x<m.y);}
xy operator >>(xy&m){return xy(x>>m.x,y>>m.y);}
xy operator &(xy&m){return xy(x &m.x,y &m.y);}
xy operator |(xy&m){return xy(x |m.x,y |m.y);}
xy operator ^(xy&m){return xy(x ^m.x,y ^m.y);}
xy operator *=(xy&m){x *=m.x;y *=m.y;return *this;}
xy operator /=(xy&m){x /=m.x;y /=m.y;return *this;}
xy operator %=(xy&m){x %=m.x;y %=m.y;return *this;}
xy operator +=(xy&m){x +=m.x;y +=m.y;return *this;}
xy operator -=(xy&m){x -=m.x;y -=m.y;return *this;}
xy operator <<=(xy&m){x<<=m.x;y<<=m.y;return *this;}
xy operator >>=(xy&m){x>>=m.x;y>>=m.y;return *this;}
xy operator &=(xy&m){x &=m.x;y &=m.y;return *this;}
xy operator |=(xy&m){x |=m.x;y |=m.y;return *this;}
xy operator ^=(xy&m){x ^=m.x;y ^=m.y;return *this;}
xy operator *(int m){return xy(x *m,y *m);}
xy operator /(int m){return xy(x /m,y /m);}
xy operator %(int m){return xy(x %m,y %m);}
xy operator +(int m){return xy(x +m,y +m);}
xy operator -(int m){return xy(x -m,y -m);}
xy operator <<(int m){return xy(x<m);}
xy operator >>(int m){return xy(x>>m,y>>m);}
xy operator &(int m){return xy(x &m,y &m);}
xy operator |(int m){return xy(x |m,y |m);}
xy operator ^(int m){return xy(x ^m,y ^m);}
xy operator *=(int m){x *=m;y *=m;return *this;}
xy operator /=(int m){x /=m;y /=m;return *this;}
xy operator %=(int m){x %=m;y %=m;return *this;}
xy operator +=(int m){x +=m;y +=m;return *this;}
xy operator -=(int m){x -=m;y -=m;return *this;}
xy operator <<=(int m){x<<=m;y<<=m;return *this;}
xy operator >>=(int m){x>>=m;y>>=m;return *this;}
xy operator &=(int m){x &=m;y &=m;return *this;}
xy operator |=(int m){x |=m;y |=m;return *this;}
xy operator ^=(int m){x ^=m;y ^=m;return *this;}
bool operator <(xy&m){return((unsigned(x) unsigned(m.y)));}
bool operator >(xy&m){return((unsigned(x) >unsigned(m.x))&&(unsigned(y) >unsigned(m.y)));}
bool operator <=(xy&m){return((unsigned(x)<=unsigned(m.x))&&(unsigned(y)<=unsigned(m.y)));}
bool operator >=(xy&m){return((unsigned(x)>=unsigned(m.x))&&(unsigned(y)>=unsigned(m.y)));}
bool operator ==(xy&m){return((unsigned(x)==unsigned(m.x))&&(unsigned(y)==unsigned(m.y)));}
bool operator <(int m){return((unsigned(x) unsigned(m)));}
bool operator >(int m){return((unsigned(x) >unsigned(m))&&(unsigned(y) >unsigned(m)));}
bool operator <=(int m){return((unsigned(x)<=unsigned(m))&&(unsigned(y)<=unsigned(m)));}
bool operator >=(int m){return((unsigned(x)>=unsigned(m))&&(unsigned(y)>=unsigned(m)));}
bool operator ==(int m){return((unsigned(x)==unsigned(m))&&(unsigned(y)==unsigned(m)));}
xy operator !(){return xy( !x, !y);}
xy operator ~(){return xy( ~x, ~y);}
xy operator +(){return xy( +x, +y);}
xy operator -(){return xy( -x, -y);}
xy get_number(){
xy m=0;
if(x>0)m.x=+x;if(x<0)m.x=-x;
if(y>0)m.y=+y;if(y<0)m.y=-y;
return m;
}
xy get_flag(){
xy m=0;
if(x>0)m.x=+1;if(x<0)m.x=-1;
if(y>0)m.y=+1;if(y<0)m.y=-1;
return m;
}
int sqrt_xx_yy(){
return sqrt(xx_yy());
}
void x_y(){
int v=x;x=y;y=v;
}
int xx(){return x*x;}
int yy(){return y*y;}
int xx_yy(){
return (x*x+y*y);
}
xy operator =(xy&m){
x=m.x;
y=m.y;
return *this;
}
xy operator =(int m){
x=m;
y=m;
return *this;
}
xy operator ++(int){
xy temp=*this;
++x;
++y;
return temp;
}
xy operator ++(){
x++;
y++;
return *this;
}
xy operator --(int){
xy temp=*this;
--x;
--y;
return temp;
}
xy operator --(){
x--;
y--;
return *this;
}
};
struct min_max{
int min;
int max;
void set(int v){
if(min>v)min=v;
if(maxv;
}
void init(){
min=+0x12341234;
max=-0x12341234;
}
};
int fill(xy*sa,int sn,xy*da){
xy*sb=sa+sn;
min_max ya;
ya.init();
for(xy*s=sa;sset(s->y);
if(ya.min<=ya.max){}else return 0;
min_max xa[xymax];
for(int y=ya.min;y<=ya.max;y++)xa[y-ya.min].init();
for(xy*s=sa;sy-ya.min].set(s->x);
xy*db=da;
for(int y=ya.min;y<=ya.max;y++){
for(int x=xa[y-ya.min].min;x<=xa[y-ya.min].max;x++)*db++=xy(x,y);
}
return (db-da);
}
int paint_line(xy r,xy *da){
// float->int (f+0.5)
// [-0.5,+0.5)=0
// [+0.5,+1.5)=1
// [+1.5,+2.5)=2
// x*a+b*y=0;
// (x+v)*a=x*a+v*a;
// (y+v)*a=y*a+v*a;
xy n=r.get_number();
xy f=r.get_flag();
xy nn=n*2;
xy d=0;
xy*db=da;
*db++=d;
if(n.y<n.x){
int v=n.x;
while(d.x!=r.x){
d.x+=f.x;
v-=nn.y;
if(v<0){
v+=nn.x;
d.y+=f.y;
}
*db++=d;
}
}else{
int v=n.y;
while(d.y!=r.y){
d.y+=f.y;
v-=nn.x;
if(v<0){
v+=nn.y;
d.x+=f.x;
}
*db++=d;
}
}
return (db-da);
}
int paint_line(xy a,xy b,xy *da){
int dn=paint_line(b-a,da);
for(int i=0;ia;
return dn;
}
int fill_line(xy r,xy*da,int w){
if(r.x==0&&r.y==0)return 0;
if(w<0)return 0;
if(w==1)return paint_line(r,da);
w/=2;//////////////
const int rl=r.sqrt_xx_yy();
xy l(w*r.x/rl,w*r.y/rl);
xy a(-l.y,+l.x);
xy b(+l.y,-l.x);
xy c=b+r;
xy d=a+r;
xy sa[xymax*4];
xy*sb=sa;
sb+=paint_line(a,b,sb);
sb+=paint_line(b,c,sb);
sb+=paint_line(c,d,sb);
sb+=paint_line(d,a,sb);
return fill(sa,sb-sa,da);////////////
xy*db=da;
for(xy*s=sa;ss;
return (db-da);
}
int fill_line(xy a,xy b,xy *da,int w){
int dn=fill_line(b-a,da,w);
for(int i=0;ia;
return dn;
}
int paint_circle(int r,xy*da){
// x*x+y*y=r*r
// (x+v)*(x+v)=x*x+2*x*v+v*v
// (y+v)*(y+v)=y*y+2*y*v+v*v
if(1<=r){}else return 0;
r*=2;///////////
xy*db=da;
{
xy d(0,r-1);
*db++=d;
int z=d.x*d.x+d.y*d.y-r*r;// x*x+y*y-r*r
do{
z+=(d.x+1)<<2;// 2*d.x*2+2*2;
d.x+=2;
if(01<d.y){
do{
z+=(-d.y+1)<<2;// -2*d.y*2+2*2
d.y-=2;
*db++=d;
}while(01<d.y);
}else{
*db++=d;
}
}while(d.x<r);
}
for(xy*d=da;d){
d->x>>=1;
d->y=(d->y+1)>>1;
}
for(xy*dc=db,*d=db;--d>=da;)*db++=xy(+d->x,-d->y);
for(xy*dc=db,*d=db;--d> da;)*db++=xy(-d->x,+d->y);
return db-da;
}
int paint_circle(xy o,int r,xy*da){
int dn=paint_circle(r,da);
for(int i=0;io;
return dn;
}
int fill_circle(int r,xy*da){
xy sa[xymax*2];
int sn=paint_circle(r,sa);
return fill(sa,sn,da);
}
int fill_circle(xy o,int r,xy*da){
int dn=fill_circle(r,da);
for(int i=0;io;
return dn;
}
int paint_ellipse(xy r,xy*da){
// x*x/(a*a)+y*y/(b*b)=1
// x*x*b*b+y*y*a*a=a*a*b*b
// x*x*b*b+y*y*a*a-a*a*b*b=0
// a*a*(x+v)*(x*v)=a*a*(x*x+2*x*v+v*v)=x*x*a*a+a*a*(2*x*v+v*v)
// a*a*(y+v)*(y*v)=a*a*(y*y+2*y*v+v*v)=y*y*a*a+a*a*(2*y*v+v*v)
// int i
// float (i-0.5,i+0.5]
r=r.get_number();//abs
if(r>=1){}else return 0;
xy*db=da;
xy rn=r.get_number();
if(rn.y<rn.x){
{
// bb*xx+aa*yy=aa*bb
const int a=r.x*2;
const int b=r.y*2;
const __int64 aa=a*a;
const __int64 bb=b*b;
xy d;
d.x=0;
d.y=b-1;
*db++=d;
__int64 z=bb*d.x*d.x+aa*d.y*d.y-aa*bb;
do{
z+=bb*((d.x+1)<<2);// 2*d.x*2+2*2;
d.x+=2;
if(01<d.y){
do{
z+=aa*((-d.y+1)<<2);// -2*d.y*2+2*2
d.y-=2;
*db++=d;
}while(01<d.y);
}else{
*db++=d;
}
}while(d.x<a);
}
for(xy*d=da;d){
d->x>>=1;
d->y=(d->y+1)>>1;
}
}else{
{
// bb*xx+aa*yy=aa*bb
const int a=r.y*2;
const int b=r.x*2;
const __int64 aa=a*a;
const __int64 bb=b*b;
xy d;
d.y=0;
d.x=b-1;
*db++=d;
__int64 z=bb*d.y*d.y+aa*d.x*d.x-aa*bb;
do{
z+=bb*((d.y+1)<<2);// 2*d.y*2+2*2;
d.y+=2;
if(01<d.x){
do{
z+=aa*((-d.x+1)<<2);// -2*d.x*2+2*2
d.x-=2;
*db++=d;
}while(01<d.x);
}else{
*db++=d;
}
}while(d.y<a);
}
for(xy*d=da;d){
d->y>>=1;
d->x=(d->x+1)>>1;
}
}
for(xy*dc=db,*d=db;--d>=da;)*db++=xy(+d->x,-d->y);
for(xy*dc=db,*d=db;--d> da;)*db++=xy(-d->x,+d->y);
return db-da;
}
int paint_ellipse(xy a,xy b,xy*da){
int dn=paint_ellipse(b-a,da);
for(int i=0;ia;
return dn;
}
int fill_ellipse(xy r,xy*da){
xy sa[xymax*2];
int sn=paint_ellipse(r,sa);
return fill(sa,sn,da);
}
int fill_ellipse(xy a,xy b,xy*da){
int dn=fill_ellipse(b-a,da);
for(int i=0;ia;
return dn;
}