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;
struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;
#define P(x) cout << (x) << "\n"
#define p(x) cout << (x)
#define all(c) (c).begin(), (c).end()
#define rall(c) (c).rbegin(), (c).rend()
#define vv(type, c, m, n, i) vector<vector<type>> c(m, vector<type>(n, i));
#define rep(i,a,n) for(int i=(a), i##_len=(n); i<i##_len; ++i)
#define rrep(i,a,n) for(int i=(a), i##_len=(n); i>i##_len; --i)
#define len(x) ((int)(x).size())
#define mp make_pair
#define eb emplace_back
#define fi first
#define se second
typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<long long> vll;
typedef vector<string> vs;
typedef vector<bool> vb;
typedef complex<double> Point;
struct Circle {
	Point c;
	double r;
	Circle(Point c = Point(0.0, 0.0), double r = 0.0) : c(c), r(r) {}
};
typedef vector<Point> Polygon;
typedef Point Vector;
typedef pair<Point, Point> Segment;
typedef Segment Line;
constexpr double EPS = (1e-9L);
enum CCW { ONLINE_FRONT = -2, CLOCKWISE, ON_SEGMENT, COUNTER_CLOCKWISE, ONLINE_BACK };
double dot(const Point& p1, const Point& p2) { return (conj(p1) * p2).real(); }
double cross(const Point& p1, const Point& p2) { return (conj(p1) * p2).imag(); }
constexpr bool eq(double a) { return abs(a) < EPS; }
bool operator <(const Point &a, const Point &b) { return real(a)!=real(b)? real(a)<real(b) : imag(a)<imag(b); }
Point project(Segment s, Point p) {
	Vector base = s.fi - s.se;
	double r = dot(p - s.fi, base) / norm(base);
	return s.fi + base * r;
}
Point reflect(Segment s, Point p) { return p + (project(s, p) - p) * 2.0; }
int ccw(const Point& p1, const Point& p2, const Point& p3) {
	Point a = p2 - p1, b = p3 - p1;
	if (cross(a, b) > EPS) return 1;
	if (cross(a, b) < -EPS) return -1;
	if (dot(a, b) < -EPS) return 2;
	if (norm(a) < norm(b)) return -2;
	return 0;
}
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.fi, s1.se, s2.fi, s2.se);
}
double getDistance(Point &a, Point &b) { return abs(a - b); }
double getDistanceLP(Line &l, Point &p) {
	return abs(cross(l.se - l.fi, p - l.fi) / abs(l.se - l.fi));
}
double getDistanceSP(Segment &s, Point &p) {
	if(dot(s.se - s.fi, p - s.fi) < 0.0) return abs(p - s.fi);
	if(dot(s.fi - s.se, p - s.se) < 0.0) return abs(p - s.se);
	return getDistanceLP(s, p);
}
double getDistance(Segment &s1, Segment &s2) {
	if(intersect(s1, s2)) return 0.0;
	return min(min(getDistanceSP(s1, s2.fi), getDistanceSP(s1, s2.se)),
				min(getDistanceSP(s2, s1.fi), getDistanceSP(s2, s1.se)));
}
Point getCrossPoint(Segment s1, Segment s2) {
	Vector base = s2.se - s2.fi;
	double d1 = abs(cross(base, s1.fi - s2.fi));
	double d2 = abs(cross(base, s1.se - s2.fi));
	double t = d1 / (d1 + d2);
	return s1.fi + (s1.se - s1.fi) * t;
}
pair<Point, Point> getCrossPoints(Circle c, Line l) {
	Vector pr = project(l, c.c);
	Vector e = (l.se - l.fi) / abs(l.se - l.fi);
	double base = sqrt(c.r * c.r - norm(pr - c.c));
	return mp(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) / (2.0 * c1.r * d));
	double t = arg(c2.c - c1.c);
	return mp(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}
int contains(Polygon g, Point p) {
	int n = len(g);
	bool x = false;
	Point a, b;
	rep(i, 0, n) {
		a = g[i] - p;
		b = g[(i + 1) % n] - p;
		if(abs(cross(a, b)) < EPS && dot(a, b) < EPS) return 1;
		if(a.imag() > b.imag()) swap(a, b);
		if(a.imag() < EPS && EPS < b.imag() && cross(a, b) > EPS) x = !x;
	}
	return (x ? 2 : 0);
}
int main() {
	cout << setprecision(10) << fixed;
	int n; cin >> n;
	Polygon pg(n);
	double x, y;
	rep(i, 0, n) {
		cin >> x >> y;
		pg[i] = Point(x, y);
	}
	int q; cin >> q;
	rep(i, 0, q) {
		cin >> x >> y;
		P(contains(pg, Point(x, y)));
	}
	return 0;
}