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
// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define all(v) v.begin(), v.end()
#define Graph vector< vector<int> >
typedef long long ll;
typedef pair<int, int> P;
const int INF = 1000000007;

const double EPS = 1e-10;
#define equals(a, b) (fabs((a) - (b)) < EPS)

struct Point{
    double x, y;
    Point(){}
    Point(double x0, double y0){
        x = x0; y = y0;
    }

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

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

    bool operator < (const Point &p){
        return x != p.x ? x < p.x : y < p.y ;
    }

};

double norm(Point p){
    return p.x * p.x + p.y * p.y;
}

double v_abs(Point p){
    return sqrt(norm(p));
}

typedef Point Vector;

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;
}

struct Circle{
    Point c;
    double r;
    Circle(){}
    Circle(Point c0, double r0){
        c.x = c0.x;
        c.y = c0.y;
        r = r0;
    }
    Circle(double x0, double y0, double r0){
        c.x = x0;
        c.y = y0;
        r = r0;
    }
};

int N;
vector<Point> G(110);
int contains(Point p){
    bool con = false;
    for(int i = 0; i < N; i++){
        Vector a = G[i] - p, b = G[i + 1] - p; // G[(i + 1) % N]
        if(equals(cross(a, b), 0.0) && dot(a, b) < EPS) return 1;
        if(a.y > b.y) swap(a, b);
        if(b.y > EPS && a.y < EPS && cross(a, b) > EPS) con = !con;
    }
    if(con) return 2;
    else return 0;
}

int main(){
    cin >> N;
    rep(i, N) cin >> G[i].x >> G[i].y;
    G[N] = G[0]; 

    int Q;
    cin >> Q;
    rep(i, Q){
        Point p;
        cin >> p.x >> p.y;
        cout << contains(p) << endl;
    }
}
