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 <bits/stdc++.h>
using namespace std;

#define EPS (1e-10)
#define equals(a,b) (fabs((a)-(b))<EPS)

class Point{
    public:
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
    Point operator+(const Point &p){
        return Point(x+p.x,y+p.y);
    }
    Point operator-(const Point &p){
        return Point(x-p.x,y-p.y);
    }
    Point operator*(const double &a){
        return Point(a*x,a*y);
    }
    Point operator/(const double &a){
        return Point(x/a,y/a);
    }
    double abs(){
        return sqrt(norm());
    }
    double norm(){
        return x*x+y*y;
    }
    bool operator<(const Point &p){
        return x!=p.x?x<p.x:y<p.y;
    }
    bool operator==(const Point &p){
        return fabs(x-p.x)<EPS&&fabs(y-p.y)<EPS;
    }
};
typedef Point Vector;
struct Segment{
    Point p1,p2;
    Segment(){}
    Segment(Point p1,Point p2):p1(p1),p2(p2){}
};
typedef Segment Line;

class Circle{
    public:
    Point c;
    double r;
    Circle(Point c=Point(),double r=0):c(c),r(r){}
};

typedef vector<Point> Polygon;

double dot(Vector a,Vector b){
    return a.x*b.x+a.y*b.y;
}

double cross(Vector a,Vector b){
    return a.x*b.y-a.y*b.x;
}

bool isOrthogonal(Segment s1,Segment s2){
    return equals(dot(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

bool isParallel(Segment s1,Segment s2){
    return equals(cross(s1.p2-s1.p1,s2.p2-s2.p1),0.0);
}

Point project(Segment s,Point p){
    Vector base=s.p2-s.p1;
    double r=dot(p-s.p1,base)/base.norm();
    return s.p1+base*r;   
}

Point reflect(Segment s,Point p){
    return p+(project(s,p)-p)*2;
}

double getDistanceLP(Line l,Point p){
    return abs(cross(l.p2-l.p1,p-l.p1))/(l.p2-l.p1).abs();
}

double getDistanceSP(Segment s,Point p){
    if(dot(s.p2-s.p1,p-s.p1)<0){
        return (p-s.p1).abs();
    }
    if(dot(s.p1-s.p2,p-s.p2)<0){
        return (p-s.p2).abs();
    }
    return getDistanceLP(s,p);
}

int ccw(Point p0,Point p1,Point p2){
    Vector a=p1-p0;
    Vector b=p2-p0;
    if(cross(a,b)>EPS) return 1;
    if(cross(a,b)<-EPS) return -1;
    if(dot(a,b)<-EPS) return 2;
    if(a.norm()<b.norm()) return -2;
    return 0;
}

bool intersect(Point p1,Point p2,Point p3,Point p4){
    return (ccw(p1,p2,p3)*ccw(p1,p2,p4)<=0&&
        ccw(p3,p4,p1)*ccw(p3,p4,p2)<=0);
}

bool intersect(Segment s1,Segment s2){
    return intersect(s1.p1,s1.p2,s2.p1,s2.p2);
}

double getDistance(Segment s1,Segment s2){
    if(intersect(s1,s2)) return 0;
    return min(min(getDistanceSP(s1,s2.p1),getDistanceSP(s1,s2.p2)),
        min(getDistanceSP(s2,s1.p1),getDistanceSP(s2,s1.p2)));
}

Point getCrossPoint(Segment s1,Segment s2){
    Vector base=s2.p2-s2.p1;
    double d1=abs(cross(base,s1.p1-s2.p1));
    double d2=abs(cross(base,s1.p2-s2.p1));
    double t=d1/(d1+d2);
    return s1.p1+(s1.p2-s1.p1)*t;
}

bool intersect(Circle c,Line l){
    double x=getDistanceLP(l,c.c);
    return (x<=c.r);    
}

pair<Point,Point> getCrossPoints(Circle c,Line l){
    assert(intersect(c,l));
    Vector pr=project(l,c.c);
    Vector e=(l.p2-l.p1)/(l.p2-l.p1).abs();
    double base=sqrt(c.r*c.r-(pr-c.c).norm());
    return make_pair(pr+e*base,pr-e*base);
}

double arg(Vector p){
    return atan2(p.y,p.x);
}

Vector polar(double a,double r){
    return Point(a*cos(r),a*sin(r));
}

bool intersect(Circle c1,Circle c2){
    int x=(c1.c-c2.c).abs();
    return (abs(c1.r-c2.r)<=x&&x<=(c1.r+c2.r));
}

pair<Point,Point> getCrossPoints(Circle c1,Circle c2){
    assert(intersect(c1,c2));
    double d=(c1.c-c2.c).abs();
    double a=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));
    double t=arg(c2.c-c1.c);
    return make_pair(c1.c+polar(c1.r,t+a),c1.c+polar(c1.r,t-a));
}

int contains(Polygon g,Point p){
    int n=g.size();
    bool x=false;
    for(int i=0;i<n;i++){
        Point a=g[i]-p,b=g[(i+1)%n]-p;
        if(abs(cross(a,b))<EPS&&dot(a,b)<EPS) return 1;
        if(a.y>b.y) swap(a,b);
        if(a.y<EPS&&EPS<b.y&&cross(a,b)>EPS) x=!x;
    }
    return (x?2:0);
}

int main(){
    Polygon g;
    int gn;
    cin>>gn;
    Point a,b;
    for(int i=0;i<gn;i++){
        cin>>a.x>>a.y;
        g.push_back(a);
    }

    int q;
    cin>>q;
    for(int i=0;i<q;i++){
        cin>>b.x>>b.y;
        cout<<contains(g,b)<<endl;
    }
}
