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 <algorithm>
#include <vector>
#include <cfloat>
#include <string>
#include <cmath>
#include <set>
#include <cstdlib>
#include <map>
#include <ctime>
#include <iomanip>
#include <functional>
#include <deque>
#include <iostream>
#include <cstring>
#include <queue>
#include <cstdio>
#include <stack>
#include <climits>
#include <sys/time.h>
#include <cctype>

using namespace std;

typedef long long ll;


#define EPS (1e-10)
#define equals(a, b) (fabs((a)-(b)) < EPS)

class Point {
 public:
  double x, y;

  Point(double x = 0, double y = 0): x(x), y(y) {}

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

  double norm() { return x*x+y*y; }
  double abs() { return sqrt(norm()); }

  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) < EPS && fabs(y-p.y) < EPS;
  }
};

typedef Point Vector;
typedef vector <Vector> Polygon;

class Segment {
 public:
  Point p1, p2;

  Segment(Point p1 = Point(), Point p2 = Point()): p1(p1), p2(p2) {}
};

typedef Segment Line;

double norm(Vector a) {
  return a.x*a.x+a.y*a.y;
}

double abs(Vector a) {
  return sqrt(norm(a));
}

// ?????????|a||b|cos
double cross(Vector a, Vector b) {
  return a.x*b.y-a.y*b.x;
}
// ?????????|a||b|sin
double dot(Vector a, Vector b) {
  return a.x*b.x+a.y*b.y;
}

// 1:???????¨??????? -1:????¨??????? 2:p2-p0-p1 -2:p0-p1-p2 0:p2???p0-p1???
int ccw(Point p0, Point p1, Point p2) {
  Vector a = p1-p0;
  Vector b = p2-p0;
  if (cross(a, b) > EPS) return 1;
  if (cross(a, b) < -EPS) return -1;
  if (dot(a, b) < -EPS) return 2;
  if (a.norm() < b.norm()) return -2;

  return 0;
}

// ??????(??¢???????????\????????¢?????´??????????????????):????????????????????????????????????????°????????§???¢?????????
Polygon andrewScan(Polygon s) {
  Polygon u, l;
  if (s.size() < 3) return s;
  sort(s.begin(), s.end());
  u.push_back(s[0]);
  u.push_back(s[1]);
  l.push_back(s[s.size()-1]);
  l.push_back(s[s.size()-2]);

  // ??????????????¨?????????
  for (int i = 2; i < s.size(); i++) {
    for (int n = u.size(); n >= 2 && ccw(u[n-2], u[n-1], s[i]) != -1; n--) {
      u.pop_back();
    }
    u.push_back(s[i]);
  }

  // ??????????????¨?????????
  for (int i = s.size()-3; i >= 0; i--) {
    for (int n = l.size(); n >= 2 && ccw(l[n-2], l[n-1], s[i]) != -1; n--) {
      l.pop_back();
    }
    l.push_back(s[i]);
  }

  // ????¨????????????????????????????????????????????????????
  reverse(l.begin(), l.end());
  for (int i = u.size()-2; i >= 1; i--) l.push_back(u[i]);

  return l;
}

// ????§???¢???????????????????????????3?????\??????????????\?????§????????????????????¨????????¶???
bool isConvex(Polygon s) {
  int n = s.size();
  int a;
  for (int i = 0; i < n; i++) {
    a = ccw(s[i], s[(i+1)%n], s[(i+2)%n]);
    if (abs(a) == 1) break;
  }
  for (int i = 0; i < n; i++) {
    int b = ccw(s[i], s[(i+1)%n], s[(i+2)%n]);
    if (a*b < 0 && abs(b) == 1) {
      return false;
    }
  }
  return true;
}

// ????§???¢g??¨????????¢??????2:?????´???1:?????????0:?????´
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 (abs(cross(a, b)) < EPS && dot(a, b) < EPS) 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() {
  Polygon poly;
  int n;
  cin >> n;
  for (int i = 0; i < n; i++) {
    int x, y;
    cin >> x >> y;
    poly.push_back(Vector(x, y));
  }
  int q;
  cin >> q;
  for (int i = 0; i < q; i++) {
    Vector p;
    cin >> p.x >> p.y;
    cout << contains(poly, p) << endl;
  }
}