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;

const double EPS = 1e-8;
const double INF = 1e12;
const double PI = acos(-1);

using Point = complex<double>;
using Polygon = vector<Point>;

inline int sgn(const double &a) { return (a < -EPS ? -1 : (a > EPS ? 1 : 0)); }

inline bool eq(const Point &a, const Point &b) { return abs(a - b) < EPS; }

namespace std {
inline bool operator<(const Point &a, const Point &b) {
    if (sgn(a.real() - b.real()))
        return sgn(a.real() - b.real()) < 0;
    return sgn(a.imag() - b.imag()) < 0;
}
} // namespace std

double dot(const Point &a, const Point &b) { return real(conj(a) * b); }

double det(const Point &a, const Point &b) { return imag(conj(a) * b); }

struct Line {
    Point p1, p2;

    Line(Point p1 = Point(), Point p2 = Point()) : p1(p1), p2(p2) {}

    bool operator<(const Line &rhs) const {
        if (eq(p2, rhs.p2))
            return p1 < rhs.p1;
        return p2 < rhs.p2;
    }
    bool operator==(const Line &rhs) const {
        return (eq(p1, rhs.p1) && eq(p2, rhs.p2)) ||
               (eq(p1, rhs.p2) && eq(p2, rhs.p1));
    }
};

inline Point curr(const Polygon &p, const int &i){
    return p[i % p.size()];
}

inline Point next(const Polygon &p, const int &i){
    return p[(i+1) % p.size()];
}

inline Point prev(const Polygon &p, const int &i){
    return p[(i+p.size()-1) % p.size()];
}

enum { OUT, ON, IN };

int contains(const Polygon &poly, const Point &p){
    bool in = false;
    for(int i=0;i<poly.size();i++){
        Point a = curr(poly, i) - p, b = next(poly, i) - p;
        if(sgn(a.imag() - b.imag()) == 1)swap(a, b);
        if(sgn(a.imag()) <= 0 && sgn(b.imag()) > 0)
            if(sgn(det(a, b)) > 0)in = !in;
        if(sgn(det(a, b)) == 0 && sgn(dot(a, b)) <= 0)return ON;
    }
    return in ? IN : OUT;
}

int main(){
    int n;
    cin >> n;
    Polygon pg;
    for(int i=0;i<n;++i){
        double x, y;
        cin >> x >> y;
        Point p = Point(x, y);
        pg.push_back(p);
    }

    int q;
    cin >> q;
    for(int i=0;i<q;++i){
        double x, y;
        cin >> x >> y;
        Point p = Point(x, y);
        cout << contains(pg, p) << endl;
    }

    return 0;
}

