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
#define _USE_MATH_DEFINES
#include<iostream>
#include<cstdio>
#include<algorithm>
#include<climits>
#include<string>
#include<vector>
#include<list>
#include<map>
#include<set>
#include<cmath>
#include<queue>
#include<cstring>
#include<stack>
using namespace std;
#define EPS 1e-10
#define INF 1000000
 
struct Point{
    double x,y;
    Point(){}
    Point(double _x,double _y){
        x=_x; y=_y;
    }
    Point operator +(const Point p)const{
        return Point(x+p.x,y+p.y);
    }
    Point operator -(const Point p)const{
        return Point(x-p.x,y-p.y);
    }
    Point operator *(const double d)const{
        return Point(x*d,y*d);
    }
    bool operator <(const Point &p)const{
        if(x==p.x) return y<p.y;
        return x<p.x;
    }
    double norm(){
        return x*x+y*y;
    }
	bool input(){
		if(cin>>x>>y) return true;
		return false;
	}
};
 
struct Line{
    Point a,b;
    Line(){}
    Line(Point _a,Point _b){
        a=_a; b=_b;
    }
	bool input(){
		if(a.input() && b.input()) return true;
		return false;
	}
};
 
struct Circle{
    Point c;
    double r;
    Circle(){}
    Circle(Point _c,double _r){
        c=_c; r=_r;
    }
};

typedef vector<Point> Polygon;

double dot(Point p,Point q){
    return p.x*q.x+p.y*q.y;
}
 
double cross(Point p,Point q){
    return p.x*q.y-q.x*p.y;
}
 
int ccw(Point a,Point b,Point c){ //a,b,c,は全て異なる
	Point v1 = Point(b-a);
	Point v2 = Point(c-a);
    if(cross(v1,v2)>EPS) return +1; //a->b->c が反時計回り
    if(cross(v1,v2)<-EPS) return -1; //a->b->c が時計回り
	if(dot(v1,v2)<-EPS) return +2; //cがa-bより後ろ c<-a->b
	if(v1.norm()<v2.norm()) return -2; //cがa-bより前 a->b->c
    return 0; //cがa-b上 a->c->b
}
 
bool intersect_ss(Line l,Line m){
    return ccw(l.a,l.b,m.a)*ccw(l.a,l.b,m.b)<=0 && ccw(m.a,m.b,l.a)*ccw(m.a,m.b,l.b)<=0;
}
 
bool crosspoint_ll(Line l,Line m,Point &p){
    Point a1,a2,b1,b2;
    a1 = l.b-l.a; a2 = m.b-m.a;
    b1 = m.a-l.a; b2 = l.a-m.b;
    double s1,s2;
    s1 = cross(a1,b1)/2; s2 = cross(a1,b2)/2;
    if(s1+s2<EPS) return false; //平行
    p = Point(m.a.x+a2.x*s1/(s1+s2),m.a.y+a2.y*s1/(s1+s2));
    return true;
}
 
int crosspoint_ss(Line l,Line m,Point &p){
    if(intersect_ss(l,m)==false) return 0; //交差していない
    if(crosspoint_ll(l,m,p)==true) return 1;
	return -1; //交点が無限個(平行かつ交差)
}
 
int crosspoint_cc(Circle c1,Circle c2,Point &p1,Point &p2){
    double d,a,t;
    d = sqrt((c2.c-c1.c).norm());
	if(abs(c1.c.x-c2.c.x)<EPS && abs(c1.c.y-c2.c.y)<EPS && abs(c1.r-c2.r)<EPS)
		return -1; //2つの円が重なっている
    if(d<abs(c1.r-c2.r) || c1.r+c2.r<d) return 0; //どちらかが内包している
    a = acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
    t = atan2(c2.c.y-c1.c.y,c2.c.x-c1.c.x);
    p1 = Point(c1.c.x+c1.r*cos(t+a),c1.c.y+c1.r*sin(t+a));
    p2 = Point(c1.c.x+c1.r*cos(t-a),c1.c.y+c1.r*sin(t-a));
    if(abs(p1.x-p2.x)<EPS && abs(p1.y-p2.y)<EPS) return 1; //交点が1つ
    return 2; //交点が2つ
}

int contains(Polygon g,Point p){
	Line l = Line(p,Point(INF,p.y));
	int cnt = 0, n = g.size();
	for(int i=0;i<n;i++){
		Point a = g[i]-p;
		Point b = g[(i+1)%n]-p;
		if(ccw(g[i],g[(i+1)%n],p)==0) return 1; //線分上
		if(a.y>b.y) swap(a,b);
		if(a.y<=EPS && EPS<b.y && cross(a,b)>EPS) cnt++;
	}
	if((cnt&1)==1) return 2; //内包している
	return 0; //内包していない
}
 
int main(){
	Polygon g;
	int N,Q;
	cin>>N; g.resize(N);
	for(int i=0;i<N;i++){
		g[i].input();
	}
	cin>>Q;
	for(int i=0;i<Q;i++){
		Point p;
		p.input();
		printf("%d\n",contains(g,p));
	}
}