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>

#define EPS (1e-10)
#define rep(i, a, b) for (int i = a; i < (int)(b); ++i)
#define rrep(i, a, b) for (int i = b - 1; i >= (int)(a); --i)

using namespace std;
using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using vd = vector<double>;
using vvi = vector<vi>;

constexpr int MOD = 1000000007;

// Data structures.
struct Point {
    double x, y;
    Point(double x = 0, double y = 0) : x(x), y(y) {}
    Point(const Point& p) : x(p.x), y(p.y) {}

    Point operator+(const Point& p) const { return Point(x + p.x, y + p.y); }
    Point operator-(const Point& p) const { return Point(x - p.x, y - p.y); }
    Point operator*(double k) const { return Point(k * x, k * y); }
    Point operator/(double k) const { return Point(x / k, y / k); }

    bool operator<(const Point& p) const { return x != p.x ? x < p.x : y < p.y; }
    bool operator==(const Point& p) const { return fabs(x - p.x) < 1e-10 && fabs(y - p.y) < 1e-10; }

    static double norm(const Point& p) { return sqrt(p.x * p.x + p.y * p.y); }
    static double dot(const Point& p1, const Point& p2) { return p1.x * p2.x + p1.y * p2.y; }
    static double cross(const Point& p1, const Point& p2) { return p1.x * p2.y - p1.y * p2.x; }
};
struct Segment {
    Point s, t;
    Segment(const Point& s, const Point& t) : s(s), t(t) {}
    Segment(const Segment& seg) : s(seg.s), t(seg.t) {}
};

typedef vector<Point> Polygon;

int ccw(const Point& p1, const Point& p2, const Point& p) {
    double cr = Point::cross(p2 - p1, p - p1);
    if (cr > 0) return 1;
    if (cr < 0) return -1;
    // p, p1, p2.
    if (Point::dot(p2 - p1, p - p1) < 0) { return 2; }
    // p1, p2, p.
    if (Point::dot(p - p2, p1 - p2) < 0) { return -2; }
    // p is in [p1, p2].
    return 0;
}

bool intersect(const Segment& s1, const Segment& s2) {
    bool ok1 = ccw(s1.s, s1.t, s2.s) * ccw(s1.s, s1.t, s2.t) <= 0;
    bool ok2 = ccw(s2.s, s2.t, s1.s) * ccw(s2.s, s2.t, s1.t) <= 0;
    return ok1 && ok2;
}

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 (ccw(g[i], g[(i + 1) % n], p) < EPS) { return 1; }
        if (a.y > b.y) swap(a, b);
        if (a.y < EPS && EPS < b.y && Point::cross(a, b) > EPS) x = !x;
    }
    return (x ? 2 : 0);
}

int check_containment(const Polygon& poly, const Point p) {
    int n = poly.size();
    bool ans = false;

    rep(i, 0, n) {
        Point s(poly[i]), t(poly[(i + 1) % n]);
        if (ccw(s, t, p) == 0) { return 1; }
        if (s.y > t.y) { swap(s, t); }
        if (s.y < p.y + EPS && p.y + EPS < t.y && Point::cross(s - p, t - p) > EPS) { ans = !ans; }
    }
    return ans ? 2 : 0;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;

    Polygon poly(n);
    rep(i, 0, n) { cin >> poly[i].x >> poly[i].y; }

    int q;
    cin >> q;
    rep(i, 0, q) {
        Point p;
        cin >> p.x >> p.y;
        cout << check_containment(poly, p) << endl;
    }

    return 0;
}
