Problem:
Polygon-Point-Containment

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.

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".

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.

Sample Input

4
0 0
3 1
2 3
0 3
3
2 1
0 2
3 2

Sample Output

2
1
0

Solution in C++14 (judge verdict: Accepted)

#include <bits/stdc++.h>

using ld = long double;
using point = std::complex<ld>;
using polygon = std::vector<point>;

constexpr ld eps = 1e-10;
constexpr ld pi = std::acos(-1.0);

bool comp(point a, point b) {
    return std::real(a) < std::real(b) || (std::real(a) <= std::real(b) && std::imag(a) < std::imag(b));
}

std::vector<point> unique(std::vector<point> ps) {
    std::sort(std::begin(ps), std::end(ps), comp);
    std::vector<point> res;
    for(auto& p : ps) {
        if(res.empty() || abs(res.back() - p) > eps) {
            res.push_back(p);
        }
    }
    return res;
}

ld dot(point const& a, point const& b) {
    return std::real(std::conj(a) * b);
}
ld cross(point const& a, point const& b) {
    return std::imag(std::conj(a) * b);
}

int ccw(point a, point b, point c) {
    b -= a; c -= a;
    if(cross(b, c) > eps) return 1;            // a -> b -> c : counterclockwise
    if(cross(b, c) < -eps) return -1;          // a -> b -> c : clockwise
    if(dot(b, c) < 0) return 2;                // c -> a -> b : line
    if(std::norm(b) < std::norm(c)) return -2; // a -> b -> c : line
    return 0;                                  // a -> c -> b : line
}

struct segment {
    segment() : a(0, 0), b(0, 0) {}
    segment(point a, point b) : a(a), b(b) {}
    point a, b;
};

struct line {
    line() : a(0, 0), b(0, 0) {}
    line(point a, point b) : a(a), b(b) {}
    line(segment s) : a(s.a), b(s.b) {}
    point a, b;
};


bool isis_ll(line l, line m) {
    return cross(l.b - l.a, m.b - m.a) < eps;
}

bool isis_ls(line l, segment s) {
    return (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

bool isis_lp(line l, point p) {
    return (std::abs(cross(l.b - p, l.a - p)) < eps);
}

bool isis_sp(segment s, point p) {
    return (std::abs(s.a - p) + std::abs(s.b - p) - std::abs(s.b - s.a) < eps);
}

bool isis_ss(segment s, segment t) {
    return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0
        && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

point proj(line l, point p) {
    long double t = dot(p - l.a, l.a - l.b) / std::norm(l.a - l.b);
    return l.a + t * (l.a - l.b);
}

point is_ll(line s, line t) {
    point sv = s.b - s.a, tv = t.b - t.a;
    assert(cross(sv, tv) != 0);
    return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

point is_ss(segment s1, segment s2) {
    assert(isis_ss(s1, s2));
    point sv = s1.b - s1.a, tv = s2.b - s2.a;
    if(cross(sv, tv) == 0) {
        if(std::abs(s1.a - s2.a) < eps || std::abs(s1.a - s2.b) < eps) {
            return s1.a;
        } else {
            return s1.b;
        }
    } else {
        return is_ll(line(s1), line(s2));
    }
}

long double dist_lp(line l, point p) {
    return std::abs(p - proj(l, p));
}

long double dist_ll(line l, line m) {
    return isis_ll(l, m) ? 0 : dist_lp(l, m.a);
}

long double dist_ls(line l, segment s) {
    return isis_ls(l, s) ? 0 : std::min(dist_lp(l, s.a), dist_lp(l, s.b));
}

long double dist_sp(segment s, point p) {
    point r = proj(line(s), p);
    return isis_sp(s, r) ? std::abs(r - p) : std::min(std::abs(s.a - p), std::abs(s.b - p));
}

long double dist_ss(segment s, segment t) {
    if(isis_ss(s, t)) return 0;
    long double d1 = std::min(dist_sp(s, t.a), dist_sp(s, t.b));
    long double d2 = std::min(dist_sp(t, s.a), dist_sp(t, s.b));
    return std::min(d1, d2);
}

ld area(polygon const& p) {
    const int N = p.size();
    ld res = 0;
    for(int i=0; i<N; ++i) {
        res += cross(p[i], p[(i+1)%N]);
    }
    return res / 2;
}

// 0 -> on, 1 -> in, 2 -> out
int is_in_polygon(polygon const& poly, point p) {
    const int n = poly.size();
    ld sum = 0;
    for(int i = 0; i < n; ++i) {
        point p1 = poly[i], p2 = poly[(i + 1) % n];
        if(isis_sp(segment(p1, p2), p)) {
            return 0;
        }
        sum += arg((p2 - p) / (p1 - p));
    }
    return std::abs(sum) < pi / 2 ? 2 : 1; // @todo: should check < 0.5 ?
}


using namespace std;

int main() {
    int g;
    cin >> g;
    polygon poly(g);
    for(int i = 0; i < g; ++i) {
        ld x, y; cin >> x >> y;
        poly[i] = point(x, y);
    }
    int q;
    cin >> q;
    while(q--) {
        ld x, y;
        cin >> x >> y;
        int ans = is_in_polygon(poly, point(x, y));
        if(ans == 2) {
            cout << 0 << endl;
        } else if(ans == 1) {
            cout << 2 << endl;
        } else {
            cout << 1 << endl;
        }
    }
}