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 <iostream>
#include <utility>
#include <vector>
#include <cmath>

using namespace std;

/*
 * cross product
 */

const double EPS = 1e-8;

typedef pair<double, double> pt;
#define x first
#define y second

pt operator-(pt a, pt b) {
  return pt(a.x - b.x, a.y - b.y);
}

bool zero(double x) {
  return fabs(x) <= EPS;
}

double cross(pt a, pt b) {
  return a.x*b.y - a.y*b.x;
}

double dot(pt a, pt b){
    return b.x*a.x + b.y*a.y;
}

bool ccw(pt a, pt b, pt c) {
  return cross(b - a, c - a) >= 0;
}

/*
 * segment segment intersection
 */

typedef pair<pt, pt> seg;
#define a first
#define b second

bool collinear(seg a, seg b) { // all four points collinear
    cout << a.a.x << " " << a.a.y << endl;
    cout << a.b.x << " " << a.b.y << endl;
    
    cout << b.a.x << " " << b.a.y << endl;
    cout << b.b.x << " " << a.b.y << endl;

    return zero(cross(a.b - a.a, b.a - a.a)) &&
           zero(cross(a.b - a.a, b.b - a.a));
}

double sq(double a) { return a * a; }

double dist(pt p, pt q) {
  return sqrt(sq(p.x - q.x) + sq(p.y - q.y));
}

int intersect(seg a, seg b) {
    if (ccw(a.a, a.b, b.a) != ccw(a.a, a.b, b.b) &&
        ccw(b.a, b.b, a.a) != ccw(b.a, b.b, a.b)) return 1;

    return 0;
 }

int inPolygon(vector<pt> polygon, pt from){
    int sum = 0;
    for (int j = 0; j < polygon.size(); ++j){
        int next = (j+1)%polygon.size();

        pt inf = make_pair(100001, from.y);
        seg line_inf = make_pair(from, inf);
        seg line_to = make_pair(polygon[j], polygon[next]);

        pt a = polygon[j] - from; pt b = polygon[next] - from;
        if (cross(a, b) == 0 && dot(a, b) <= 0) {
            return 1;
        }
        sum += intersect(line_inf, line_to);
    }
    if (sum % 2) return 2;
    return 0;
}

int main(){

    vector<pt> polygon;
    int n;
    cin >> n;
    for (int i = 0; i < n; ++i){
        int x, y;
        cin >> x >> y;
        polygon.push_back(make_pair(x, y));
    }
    cin >> n;
    for (int i = 0; i < n; ++i){
        int p, q;
        cin >> p >> q;
        cout << inPolygon(polygon, make_pair(p, q)) << endl;

    }

    return 0;
}
