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 <complex>
#include <vector>
#include <cmath>
#include <utility>
#include <cassert>
#include <cmath>
#include <iostream>

const double EPS=1e-10;

#define equals(a, b) (fabs((a)-(b))<EPS)
#define X real()
#define Y imag()

using namespace std;

typedef complex<double> Point;
typedef complex<double> Vector;

struct Segment {
    Point p1, p2;
};
typedef Segment Line;

struct Circle {
    Point c;
    double r;
    Circle(Point c=Point(), double r=0.0) :
        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;
}

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

Point reflect(Segment s, Point p) {
    return p+(project(s,p)-p)*2.0;
}

enum CCW {
    COUNTER_CLOCKWISE=1,
    CLOCKWISE=-1,
    ONLINE_BACK=2,
    ONLINE_FRONT=-2,
    ON_SEGMENT=0,
};

int ccw(Point p0, Point p1, Point p2) {
    Vector a=p1-p0;
    Vector b=p2-p0;
    if(cross(a,b)>EPS) return CCW::COUNTER_CLOCKWISE;
    if(cross(a,b)<-EPS) return CCW::CLOCKWISE;
    if(dot(a,b)<-EPS) return CCW::ONLINE_BACK;
    if(norm(a)<norm(b)) return CCW::ONLINE_FRONT;

    return CCW::ON_SEGMENT;
}

double getDistance(Point a,Point b) {
    return abs(a-b);
}

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

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

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

    return make_pair(pr+e*base,pr-e*base);

}

pair<Point,Point> getCrossPoints(Circle c1, Circle c2) {
    double d=abs(c1.c-c2.c);
    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));
}

// IN 2, ON 1, OUT 0
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() {
    int n;
    cin>>n;
    Polygon g(n);
    for(int i=0;i<n;i++) {
        double x,y;
        cin>>x>>y;
        g[i]=Point(x,y);
    }
    int q; cin>>q;
    while(q-->0) {
        double x,y;
        cin>>x>>y;
        Point p=Point(x,y);
        cout<<contains(g,p)<<endl;
    }
}