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
from sys import stdin
import math

EPS = 1e-10

class Vector:
    def __init__(self, x=None, y=None):
        self.x = x
        self.y = y

    def __add__(self, other):
        return Vector(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Vector(self.x - other.x, self.y - other.y)

    # can't  apply "number * Vector" but "Vector * number"
    def __mul__(self, k):
        return Vector(self.x * k, self.y * k)

    def __truediv__(self, k):
        return Vector(self.x / k, self.y / k)

    def __gt__(self, other):
        return self.x > other.x and self.y > other.yb

    def __lt__(self, other):
        return self.x < other.x and self.y < other.yb

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y

    def dot(self, other):
        return self.x * other.x + self.y * other.y

    # usually cross operation return Vector but it returns scalor
    def cross(self, other):
        return self.x * other.y - self.y * other.x

    def norm(self):
        return self.x * self.x + self.y * self.y

    def abs(self):
        return math.sqrt(self.norm())

    def rotate(self, theta):
        return Vector(self.x * math.cos(theta)
                               - self.y * math.sin(theta),
                               self.x * math.sin(theta)
                               + self.y * math.cos(theta))

class Point(Vector):
    def __init__(self, *args, **kargs):
        return super().__init__(*args, **kargs)

class Segment:
    def __init__(self, p1=Point(0, 0), p2=Point(1, 1)):
        self.p1 = p1
        self.p2 = p2

class Line(Segment):
    def __init__(self, *args, **kargs):
        return super().__init__(*args, **kargs)

def ccw(p0, p1, p2):
    a = p1 - p0
    b = p2 - p0
    if a.cross(b) > EPS:
        return 1
    elif a.cross(b) < -EPS:
        return -1
    elif a.dot(b) < -EPS:
        return 2
    elif a.norm() < b.norm():
        return -2
    else:
        return 0

def contains(P, p):
    n = len(P)
    count = 0
    for i in range(n):
        a = P[i]
        b = P[ (i + 1) % n ]
        if a.y > b.y:
            a, b = b, a
        if ccw(p, a, b) == 2 or p == a or p == b:
            return 1
        if ccw(p, a, b) == 1 and b.y > p.y and a.y <= p.y:
            count = count + 1
    if count % 2 == 0:
        return 0
    else:
        return 2

def read_polygon(n):
    P = []
    for _ in range(n):
        line = stdin.readline().strip().split()
        p = Vector(int(line[0]), int(line[1]))
        P.append(p)
    return P

def read_and_print_results(k, P):
    for _ in range(k):
        line = stdin.readline().strip().split()
        p = Vector(int(line[0]), int(line[1]))
        result = contains(P, p)
        print(result)

def __main():
    n = int(input())
    P = read_polygon(n)
    k = int(input())
    read_and_print_results(k, P)

if __name__ == '__main__':
    __main()
