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 <iostream>
#include <cmath>
#include <complex>
#include <tuple>
#include <vector>
using namespace std;

using vec = complex<double>;
using line = pair<vec,vec>;
using polygon = vector<vec>;
const double eps = 0.0000001;

double inner_product(vec u,vec v){
    return real(u*conj(v));
}
double cross_product(vec u,vec v){
    return imag(conj(u)*v);
}

vec projection(line l,vec p){//p???l???????°???±
    vec s=l.first, t=l.second;
    double k = inner_product(t-s,p-s)/inner_product(t-s,t-s);
    return (1.0-k)*s+k*t;
}

vec reflection(line l,vec p){
    return 2.0*projection(l,p)-p;
}

int ccw(vec& a, vec& b, vec& c){
    vec ab = b-a, ac = c-a;
    double o = cross_product(ab,ac);
    if(o>0) return 1; //CCW
    if(o<0) return -1; //CW
    if(inner_product(ab,ac)<0){
        return 2; //C-A-B
    }else{
        if(inner_product(ab,ab)<inner_product(ac,ac)){
            return -2; //A-B-C
        }else{
            return 0; //A-C-B
        }
    }
}

bool isIntersect(line l0, line l1){
    int s = ccw(l0.first,l0.second,l1.first)*ccw(l0.first,l0.second,l1.second);
    if(s!=0&&s!=-1&&s!=-4) return false;
    s=ccw(l1.first,l1.second,l0.first)*ccw(l1.first,l1.second,l0.second);
    if(s!=0&&s!=-1&&s!=-4) return false;
    else return true;
}

vec interSection(line l0, line l1){
    vec s0, t0, s1, t1;
    tie(s0,t0)=l0; tie(s1,t1)=l1;
    double k = cross_product(t1-s1,s1-s0)/cross_product(t1-s1,t0-s0);
    return s0+(t0-s0)*k;
}

double segLength(line l){
    return abs(l.first-l.second);
}

double distLine2point(line l, vec p){
    return abs(cross_product(l.second-l.first,p-l.first))/abs(l.second-l.first);
}

double distSeg2Point(line l, vec p){
    vec x = projection(l,p);
    double L = segLength(l);
    if(abs(x-l.first)<L&&abs(x-l.second)<L){
        return abs(x-p);
    }else{
        return min(abs(l.first-p),abs(l.second-p));
    }
}

double distSeg2Seg(line l1, line l2){
    if(isIntersect(l1,l2)) return 0;
    double ret = 1e20;
    ret = min(ret,distSeg2Point(l1,l2.first));
    ret = min(ret,distSeg2Point(l1,l2.second));
    swap(l1,l2);
    ret = min(ret,distSeg2Point(l1,l2.first));
    ret = min(ret,distSeg2Point(l1,l2.second));
    return ret;
}

double area(polygon& g){
    double S=0;
    for(auto i = g.begin()+1; i!=g.end();++i){
        S += cross_product(*(i-1),*i);
    }
    S/=2;
    return S;
}

bool isConvex(polygon& g){
    int n=g.size()-2;
    for(int i=0;i<n;i++){
        if(!~ccw(g[i],g[i+1],g[i+2]))return false;
    }
    return true;
}

bool isOnEdge(polygon& g,vec& p){
    int n=g.size()-1;
    for(int i=0;i<n;i++){
        if(!ccw(g[i],g[i+1],p)) return true;
    }
    return false;
}

bool isInside(polygon& g,vec& p){
    int n=g.size()-1,c=0;
    vec O = vec(114514,123456);
    for(int i=0;i<n;i++){
        c+=isIntersect(line(O,p),line(g[i],g[i+1]));
    }
    if(c%2) return true;
    else return false;
}

//???????????§???????????????


int main(){
    int n;
    cin >> n;
    polygon g;
    while(n--){
        int x,y;
        cin>>x>>y;
        g.emplace_back(x,y);
    }
    g.push_back(g[0]);

    cout.precision(1);
    cout << fixed;

    cin >> n;
    while(n--){
        int x,y;
        cin>>x>>y;
        vec v(x,y);
        if(isOnEdge(g,v)){
            cout << 1 << endl;
        }else if(isInside(g,v)){
            cout << 2 << endl;
        }else{
            cout << 0 << endl;
        }
    }
    return 0;
}