#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
using namespace std;
//using ll=long long;
const double EPS = 1e-10;
inline bool equals(double a, double b) { return fabs(a - b) < EPS; }
const double PI = 3.141592653589793238;
class Point {
public:
	double x, y;
	Point(double x, double y) :x(x), y(y) {}
	Point() {}
	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) { return Point(x*k, y*k); }
	Point operator /(double k) { return Point(x / k, y / k); }
	void show() { printf("%.10lf %.10lf", x, y); }
};

using Vector = Point;
inline double norm(Vector a) {
	return a.x*a.x + a.y*a.y;
}
double absv(Vector a) {
	return sqrt(norm(a));
}
inline double dot(Vector a, Vector b) {
	return a.x*b.x + a.y*b.y;
}
inline double cross(Vector a, Vector b) {
	return a.x*b.y - a.y*b.x;
}
struct Segment {
	Point p1, p2;
};

using Line = Segment;
class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) :c(c), r(r) {}
};
using Polygon = vector<Point>; 
Point project(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / norm(base);
	return s.p1 + base*r;
}
Point reflect(Segment s, Point p) {
	return p + (project(s, p) - p)*2.0;
}
double getDistanceLP(Line, Point);
double getDistance(Point, Point);
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0;
	Vector b = p2 - p0;
	if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS) return CLOCKWISE;
	if (dot(a, b) < -EPS) return ONLINE_BACK;
	if (norm(a) < norm(b)) return ONLINE_FRONT;
	return ON_SEGMENT;
}
bool intersect(Point p1, Point p2, Point p3, Point p4) {
	return (ccw(p1, p2, p3)*ccw(p1, p2, p4) <= 0 and ccw(p3, p4, p1)*ccw(p3, p4, p2) <= 0);
}

bool intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
bool intersect(Circle c1, Circle c2) {
	return c1.r + c2.r >= getDistance(c1.c, c2.c);
}

bool intersect(Circle c, Line l) {
	double d = getDistanceLP(l, c.c);
	return d <= c.r;
}

double getDistance(Point a, Point b) {
	return absv(a - b);
}

double getDistanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / absv(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return absv(p - s.p1);
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return absv(p - s.p2);
	return getDistanceLP(s, p);
}

double getDistance(Segment s1,Segment s2){
	if (intersect(s1, s2)) return 0.0;
	return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPoint(Segment s1, Segment s2) {
	Vector base = s2.p2 - s2.p1;
	double d1 = abs(cross(base, s1.p1 - s2.p1));
	double d2 = abs(cross(base, s1.p2 - s2.p1));
	return s1.p1 + (s1.p2 - s1.p1)*(d1 / (d1 + d2));
}
pair<Point, Point> getCrossPoints(Circle c, Line l) {
	assert(intersect(c, l));
	Point pr = project(l, c.c);
	Vector lv = l.p2 - l.p1;
	Vector le = lv / absv(lv);
	double base = sqrt(c.r*c.r - norm(c.c - pr));
	return make_pair(pr + le*base, pr - le*base);
}
double arg(Vector p) {
	return atan2(p.y, p.x);
}
Vector polar(double a, double r) {
	return Point(a * cos(r), a * sin(r));
}

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
	assert(intersect(c1, c2));
	double d = getDistance(c1.c, c2.c);
	double a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2 * c1.r*d));
	double t = arg(c2.c - c1.c);
	return make_pair(c1.c + polar(c1.r, a + t), c1.c + polar(c1.r, t - a));
}

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; Point b = g[(i + 1) % n] - p;
		if (abs(cross(a, b)) < EPS && dot(a, b) <= 0) return 1;
		if (a.y > b.y) swap(a, b);
		if (a.y < EPS && EPS<b.y && cross(a, b)>EPS) x = !x;
	}
	return (x ? 2 : 0);
	
}
int main() {
	int n, q, x, y;
	Polygon pg;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> x >> y;
		pg.push_back(Point(x, y));
	}
	cin >> q;
	for (int i = 0; i < q; i++) {
		cin >> x >> y;
		cout << contains(pg, Point(x, y)) << endl;
	}
}
### Prompt

Please formulate a CPP solution to the following problem:

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

### Response

```cpp
#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
using namespace std;
//using ll=long long;
const double EPS = 1e-10;
inline bool equals(double a, double b) { return fabs(a - b) < EPS; }
const double PI = 3.141592653589793238;
class Point {
public:
	double x, y;
	Point(double x, double y) :x(x), y(y) {}
	Point() {}
	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) { return Point(x*k, y*k); }
	Point operator /(double k) { return Point(x / k, y / k); }
	void show() { printf("%.10lf %.10lf", x, y); }
};

using Vector = Point;
inline double norm(Vector a) {
	return a.x*a.x + a.y*a.y;
}
double absv(Vector a) {
	return sqrt(norm(a));
}
inline double dot(Vector a, Vector b) {
	return a.x*b.x + a.y*b.y;
}
inline double cross(Vector a, Vector b) {
	return a.x*b.y - a.y*b.x;
}
struct Segment {
	Point p1, p2;
};

using Line = Segment;
class Circle {
public:
	Point c;
	double r;
	Circle(Point c = Point(), double r = 0.0) :c(c), r(r) {}
};
using Polygon = vector<Point>; 
Point project(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / norm(base);
	return s.p1 + base*r;
}
Point reflect(Segment s, Point p) {
	return p + (project(s, p) - p)*2.0;
}
double getDistanceLP(Line, Point);
double getDistance(Point, Point);
static const int COUNTER_CLOCKWISE = 1;
static const int CLOCKWISE = -1;
static const int ONLINE_BACK = 2;
static const int ONLINE_FRONT = -2;
static const int ON_SEGMENT = 0;

int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0;
	Vector b = p2 - p0;
	if (cross(a, b) > EPS) return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS) return CLOCKWISE;
	if (dot(a, b) < -EPS) return ONLINE_BACK;
	if (norm(a) < norm(b)) return ONLINE_FRONT;
	return ON_SEGMENT;
}
bool intersect(Point p1, Point p2, Point p3, Point p4) {
	return (ccw(p1, p2, p3)*ccw(p1, p2, p4) <= 0 and ccw(p3, p4, p1)*ccw(p3, p4, p2) <= 0);
}

bool intersect(Segment s1, Segment s2) {
	return intersect(s1.p1, s1.p2, s2.p1, s2.p2);
}
bool intersect(Circle c1, Circle c2) {
	return c1.r + c2.r >= getDistance(c1.c, c2.c);
}

bool intersect(Circle c, Line l) {
	double d = getDistanceLP(l, c.c);
	return d <= c.r;
}

double getDistance(Point a, Point b) {
	return absv(a - b);
}

double getDistanceLP(Line l, Point p) {
	return abs(cross(l.p2 - l.p1, p - l.p1) / absv(l.p2 - l.p1));
}

double getDistanceSP(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0) return absv(p - s.p1);
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0) return absv(p - s.p2);
	return getDistanceLP(s, p);
}

double getDistance(Segment s1,Segment s2){
	if (intersect(s1, s2)) return 0.0;
	return min(min(getDistanceSP(s1, s2.p1), getDistanceSP(s1, s2.p2)), min(getDistanceSP(s2, s1.p1), getDistanceSP(s2, s1.p2)));
}

Point getCrossPoint(Segment s1, Segment s2) {
	Vector base = s2.p2 - s2.p1;
	double d1 = abs(cross(base, s1.p1 - s2.p1));
	double d2 = abs(cross(base, s1.p2 - s2.p1));
	return s1.p1 + (s1.p2 - s1.p1)*(d1 / (d1 + d2));
}
pair<Point, Point> getCrossPoints(Circle c, Line l) {
	assert(intersect(c, l));
	Point pr = project(l, c.c);
	Vector lv = l.p2 - l.p1;
	Vector le = lv / absv(lv);
	double base = sqrt(c.r*c.r - norm(c.c - pr));
	return make_pair(pr + le*base, pr - le*base);
}
double arg(Vector p) {
	return atan2(p.y, p.x);
}
Vector polar(double a, double r) {
	return Point(a * cos(r), a * sin(r));
}

pair<Point, Point> getCrossPoints(Circle c1, Circle c2) {
	assert(intersect(c1, c2));
	double d = getDistance(c1.c, c2.c);
	double a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2 * c1.r*d));
	double t = arg(c2.c - c1.c);
	return make_pair(c1.c + polar(c1.r, a + t), c1.c + polar(c1.r, t - a));
}

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; Point b = g[(i + 1) % n] - p;
		if (abs(cross(a, b)) < EPS && dot(a, b) <= 0) return 1;
		if (a.y > b.y) swap(a, b);
		if (a.y < EPS && EPS<b.y && cross(a, b)>EPS) x = !x;
	}
	return (x ? 2 : 0);
	
}
int main() {
	int n, q, x, y;
	Polygon pg;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> x >> y;
		pg.push_back(Point(x, y));
	}
	cin >> q;
	for (int i = 0; i < q; i++) {
		cin >> x >> y;
		cout << contains(pg, Point(x, y)) << endl;
	}
}
```