For a given polygon g and target points t, print "2" if g contains t, "1" if t is on a segment of g, "0" otherwise.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of the polygon. The line segment connecting pn and p1 is also a side of the polygon.

Note that the polygon is not necessarily convex.

Constraints

* 3 ≤ n ≤ 100
* 1 ≤ q ≤ 1000
* -10000 ≤ xi, yi ≤ 10000
* No point of the polygon will occur more than once.
* Two sides of the polygon can intersect only at a common endpoint.

Input

The entire input looks like:


g (the sequence of the points of the polygon)
q (the number of queris = the number of target points)
1st query
2nd query
:
qth query


g is given by coordinates of the points p1,..., pn in the following format:


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them.

Each query consists of the coordinate of a target point t. The coordinate is given by two intgers x and y.

Output

For each query, print "2", "1" or "0".

Example

Input

4
0 0
3 1
2 3
0 3
3
2 1
0 2
3 2


Output

2
1
0
#include<cstdio>
#include<cstring>
#include<vector>
#include<queue>
#include<algorithm>
#include<cmath>
#include<climits>
#include<string>
#include<set>
#include<map>
using namespace std;
#define rep(i,n) for(int i=0;i<((int)(n));i++)
#define reg(i,a,b) for(int i=((int)(a));i<=((int)(b));i++)
#define irep(i,n) for(int i=((int)(n))-1;i>=0;i--)
#define ireg(i,a,b) for(int i=((int)(b));i>=((int)(a));i--)
typedef long long int lli;
typedef pair<int,int> mp;
#define fir first
#define sec second
#define IINF INT_MAX
#define LINF LLONG_MAX

struct pos{
	double x,y;
	double norm,norm2;
	pos tov(pos a){
		return (a-(*this));
	}
	pos operator+(pos a)const{
		pos res=a;
		res.x+=x; res.y+=y;
		res=pos(res.x,res.y);
		return res;
	}
	pos operator-(pos a)const{
		pos res=(*this);
		res.x-=a.x; res.y-=a.y;
		res=pos(res.x,res.y);
		return res;
	}
	pos scalar(double a){
		pos res=(*this);
		res.x*=a; res.y*=a;
		res=pos(res.x,res.y);
		return res;
	}
	double dot(pos a){
		return x*a.x + y*a.y;
	}
	double cross(pos a){
		return x*a.y - y*a.x;
	}
	pos(double ix,double iy){
		x=ix; y=iy;
		norm2=x*x+y*y;
		norm=sqrt(norm2);
	}
	pos(){}
	string str(){
		char ns[50];
		sprintf(ns,"(%lf %lf)",x,y);
		return	string(ns);
	}
	static pos polar(double r,double t){
		return pos(r*cos(t),r*sin(t));
	}
};

struct line{
	pos p,q;
	pos vec;
	string str(){
		return ("("+p.str()+"-"+q.str()+")");
	}
	bool iscross(line a){
		double da,db;
		da=vec.cross( p.tov(a.p) );
		db=vec.cross( p.tov(a.q) );
		if(da*db>=0)return false;
		da=a.vec.cross( a.p.tov(p) );
		db=a.vec.cross( a.p.tov(q) );
		return (da*db<0);
	}
	line(pos ip,pos iq){
		p=ip; q=iq;
		vec=p.tov(q);
	}
	line(){}
	double dist(pos a){
		if(p.tov(a).dot( p.tov(q) )<0)return p.tov(a).norm;
		if(q.tov(a).dot( q.tov(p) )<0)return q.tov(a).norm;
		return abs(vec.cross(p.tov(a))/vec.norm);
	}
	double dist(line a){
		if(iscross(a))return 0;
		return min( min(dist(a.p),dist(a.q)) , min(a.dist(this->p),a.dist(this->q)));
	}
};

double lowofcos_getcos(double a,double b,double c){
	return ((a*a+b*b-c*c)/(2*a*b));
}

struct circle{
	pos p;
	double r;
	
	line getintersection(circle a){
		pos cv=p.tov(a.p);
		double br=atan2(cv.y,cv.x);
		double dr=acos(lowofcos_getcos( r, cv.norm, a.r));
		
		pos p1= p+pos::polar(r,br+dr);
		pos p2= p+pos::polar(r,br-dr);
		
		return line(p1,p2);
	}
	circle(pos ip,double ir){
		p=ip; r=ir;
	}
	circle(){}
};

struct polygon{
	vector<pos> ps;
	polygon(){}
	double area(){
		double res=0;
		rep(i,ps.size()){
			pos no=ps[i],to=ps[(i+1)%ps.size()];
			res+=(no.x+to.x)*(no.y-to.y);
		}
		return abs(res)/2;
	}
	polygon(pos a,pos b){
		ps.push_back(a);
		ps.push_back(pos(a.x,b.y));
		ps.push_back(b);
		ps.push_back(pos(b.x,a.y));
	}
	line gete(int a){
		return line(ps[a],ps[(a+1)%ps.size()]);
	}
	int isin(pos a){
		//????????¢??????
		/*
		if((a.x-ps[0].x)*(a.x-ps[2].x)>0)return false;
		if((a.y-ps[0].y)*(a.y-ps[2].y)>0)return false;
		return true;
		*/
		
		//?????´??????2,?????£????????????1,?????????0
		double as=0;
		rep(i,ps.size()){
			line ne=gete(i);
			if(ne.dist(a)<=0)return 1;
			pos v1=a.tov(ne.p);
			pos v2=a.tov(ne.q);
			//printf("%s %s\n",v1.str().c_str(),v2.str().c_str());
			double nt=acos(max(-1.0,min(v1.dot(v2)/(v1.norm*v2.norm),1.0)));
			double ns=(v1.cross(v2)/(v1.norm*v2.norm));
			//printf("%lf %lf %lf %lf %lf\n",nt,ns,v1.norm,v2.norm,v1.dot(v2));
			if(ns<0)nt*=-1;
			as+=nt;
			//printf("%d %s %lf\n",i,ne.str().c_str(),as);
		}
		if(abs(as)<1e-6)return 0;
		return 2;
	}
	
	polygon mult(polygon a){
		return a;
	}
};


int main(void){
	int n;
	scanf("%d",&n);
	polygon pl;
	rep(i,n){
		double p,q;
		scanf("%lf%lf",&p,&q);
		pl.ps.push_back(pos(p,q));
	}
	
	int qn;
	scanf("%d",&qn);
	rep(i,qn){
		double p,q;
		scanf("%lf%lf",&p,&q);
		printf("%d\n",pl.isin(pos(p,q)));
	}
	
	return 0;
}