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
# -*- coding: utf-8 -*-

import collections
import math


class Vector2(collections.namedtuple("Vector2", ["x",  "y"])):

    def __add__(self, other):
        return Vector2(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Vector2(self.x - other.x, self.y - other.y)

    def __mul__(self, scalar):
        return Vector2(self.x * scalar, self.y * scalar)

    def __neg__(self):
        return Vector2(-self.x, -self.y)

    def __pos__(self):
        return Vector2(+self.x, +self.y)

    def __abs__(self):  # norm
        return math.sqrt(float(self.x * self.x + self.y * self.y))

    def __truediv__(self, scalar):
        return Vector2(self.x / scalar, self.y / scalar)

    def abs2(self):
        return float(self.x * self.x + self.y * self.y)

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

    def cross(self, other):  # cross product
        return self.x * other.y - self.y * other.x


def getDistanceSP(segment, point):
    p = point
    p1, p2 = segment
    if (p2 - p1).dot(p - p1) < 0:
        return abs(p - p1)
    if (p1 - p2).dot(p - p2) < 0:
        return abs(p - p2)
    return abs((p2 - p1).cross(p - p1)) / abs(p2 - p1)


def getDistance(s1, s2):
    a, b = s1
    c, d = s2
    if intersect(s1, s2):  # intersect
        return 0
    return min(getDistanceSP(s1, c), getDistanceSP(s1, d), getDistanceSP(s2, a), getDistanceSP(s2, b))


def ccw(p0, p1, p2):
    a = p1 - p0
    b = p2 - p0
    if a.cross(b) > 0:
        return 1  # COUNTER_CLOCKWISE
    elif a.cross(b) < 0:
        return -1  # CLOCKWISE
    elif a.dot(b) < 0:
        return 2  # ONLINE_BACK
    elif abs(a) < abs(b):
        return -2  # ONLINE_FRONT
    else:
        return 0  # ON_SEGMENT


def intersect(s1, s2):
    a, b = s1
    c, d = s2
    return ccw(a, b, c) * ccw(a, b, d) <= 0 and ccw(c, d, a) * ccw(c, d, b) <= 0


def project(l, p):
    p1, p2 = l
    base = p2 - p1
    hypo = p - p1
    return p1 + base * (hypo.dot(base) / abs(base)**2)


class Circle():
    def __init__(self, c, r):
        self.c = c
        self.r = r


def getCrossPoints(c, l):
    pr = project(l, c.c)
    p1, p2 = l
    e = (p2 - p1) / abs(p2 - p1)
    base = math.sqrt(c.r * c.r - (pr - c.c).abs2())
    return [pr + e * base, pr - e * base]


def polar(r, a):
    return Vector2(r * math.cos(a), r * math.sin(a))


def getCrossPointsCircle(c1, c2):
    base = c2.c - c1.c
    d = abs(base)
    a = math.acos((c1.r**2 + d**2 - c2.r**2) / (2 * c1.r * d))
    t = math.atan2(base.y, base.x)
    return [c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a)]


def contains(g, p):
    n = len(g)
    x = 0
    for i in range(n):
        a = g[i] - p
        b = g[(i + 1) % n] - p
        if a.cross(b) == 0 and a.dot(b) <= 0:
            return 1
        if a.y > b.y:
            a, b = b, a
        if a.y <= 0 and b.y > 0 and a.cross(b) > 0:
            x += 1

    if x % 2 == 1:
        return 2
    else:
        return 0


if __name__ == '__main__':

    n = int(input())
    g = []
    for _ in range(n):
        a, b = map(int, input().split())
        g.append(Vector2(a, b))
    q = int(input())
    for _ in range(q):
        c, d = map(int, input().split())
        print(contains(g, Vector2(c, d)))

