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;

#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(x * a, y * a);}
    Point operator / (double a) {return Point(x / a, y / a);}

    double abs() {return sqrt(norm());}
    double norm() {return x * x + y * y;}
    
    bool operator < (const Point &p) const {
        return x != p.x ? x < p.x : y < p.y;
    }

    bool operator == (const Point &p) const{
        return equals(x, p.x) && equals(y, p.y);
    }
};typedef Point Vector;

typedef vector<Point> Polygon;

struct Segment {
    Point p1, p2;
};

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

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

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 (fabs(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(){
    int g; cin >> g;
    Polygon G;
    for (int i = 0; i < g; i++)
    {
        int x, y; cin >> x >> y;
        Point p = Point(x, y);
        G.push_back(p);
    }
    int q; cin >> q;
    for (int i = 0; i < q; i++)
    {
        int x, y; cin >> x >> y;
        Point p = Point(x, y);
        cout << contains(G, p) << endl;
    }
    
}
