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;
typedef complex<double> qua;
vector <qua> v;
const double epx = 1e-7;
int ccw(qua a,qua b, qua c)
{
    b-=a,c-=a,a=c*conj(b);
    if(a.imag()>epx) return 1;
    if(a.imag()<-epx) return -1;
    if(a.real()<-epx) return 2;
    if(abs(b)+epx<abs(c)) return -2;
    return 0;
}
double Arg(qua a,qua b,qua c)
{
    b-=a,c-=a;
    return arg(c*conj(b));
}
int inploygon(vector<qua> &ve,qua q)
{
    int n=ve.size();
    double sum=0;
    for(int i=0;i<n;i++)
    {
        if(ccw(ve[i],ve[(i+1)%n],q)==0) return 1;
        sum+=Arg(q,ve[i],ve[(i+1)%n]);
    }
    if(abs(sum)<epx) return 0;
    else return 2;
}
int main()
{
    int n,m;
    double x,y;
    scanf("%d",&n);
    while(n--)
    {
        scanf("%lf%lf",&x,&y);
        v.push_back(qua(x,y));
    }
    scanf("%d",&m);
    while(m--)
    {
        scanf("%lf%lf",&x,&y);
        printf("%d\n",inploygon(v,qua(x,y)));
    }
}

