import java.io.OutputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.FileInputStream;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.TreeSet;
import java.util.Comparator;
import java.io.InputStream;
/**
* Built using CHelper plug-in
* Actual solution is at the top
*/
public class Main {
public static void main(String[] args) {
InputStream inputStream;
try {
inputStream = new FileInputStream("robot.in");
} catch (IOException e) {
throw new RuntimeException(e);
}
OutputStream outputStream;
try {
outputStream = new FileOutputStream("robot.out");
} catch (IOException e) {
throw new RuntimeException(e);
}
InputReader in = new InputReader(inputStream);
PrintWriter out = new PrintWriter(outputStream);
robot solver = new robot();
solver.solve(1, in, out);
out.close();
}
static class robot {
private final double eps = 1e-10;
private byte[][] graph;
private boolean[] badPoint;
private double distSquare(Point a, Point b) {
return (a.x - b.x) * (a.x - b.x) +
(a.y - b.y) * (a.y - b.y);
}
private double dist(Point a, Point b) {
return Math.sqrt(distSquare(a, b));
}
private double slope(Point a, Point b) {
if (a.x == b.x) return 1e99;
return (a.y - b.y) / (a.x - b.x);
}
private double crossProduct(Point o, Point a, Point b) {
return (a.x - o.x) * (b.y - o.y) - (a.y - o.y) * (b.x - o.x);
}
public void solve(int testNumber, InputReader in, PrintWriter out) {
int N = in.nextInt();
Point[] robot = new Point[N];
for (int i = 0; i < N; ++i) {
robot[i] = new Point(in.nextDouble(), in.nextDouble());
}
int M = in.nextInt();
Point[][] obstacles = new Point[M][];
for (int i = 0; i < M; ++i) {
int K = in.nextInt();
obstacles[i] = new Point[K];
for (int j = 0; j < K; ++j)
obstacles[i][j] = new Point(in.nextDouble(), in.nextDouble());
}
for (int i = 0; i < M; ++i)
obstacles[i] = expand(obstacles[i], robot);
/*if (!Arrays.deepEquals(obstacles[0], obstacles[1]))
throw new RuntimeException();*/
double minx = robot[0].x, miny = robot[0].y;
for (int i = 1; i < N; ++i) {
minx = Math.min(minx, robot[i].x);
miny = Math.min(miny, robot[i].y);
}
//System.err.println(Arrays.toString(obstacles[0]));
Point start = new Point(minx, miny), end = new Point(in.nextDouble(), in.nextDouble());
if (!checkPoint(end, obstacles)) {
out.println(-1);
return;
}
int countPoints = 2;
for (int i = 0; i < M; ++i)
countPoints += obstacles[i].length;
Point[] allPoints = new Point[countPoints];
allPoints[0] = start;
countPoints = 1;
for (Point[] obstacle : obstacles)
for (Point p : obstacle)
allPoints[countPoints++] = p;
allPoints[countPoints++] = end;
//System.err.flush();
double ans = shortestPath(allPoints, obstacles, 0, countPoints - 1);
out.println(ans != -1 ? String.format("%.2f", ans) : "-1");
}
private Point[] expand(Point[] poly1, Point[] poly2) {
int N = poly1.length, M = poly2.length;
double minx = poly2[0].x, miny = poly2[0].y;
for (int i = 1; i < M; ++i) {
minx = Math.min(minx, poly2[i].x);
miny = Math.min(miny, poly2[i].y);
}
Point[] allPoints = new Point[N * M];
for (int i = 0; i < N; ++i) {
for (int j = 0; j < M; ++j) {
double nx = poly1[i].x - poly2[j].x + minx;
double ny = poly1[i].y - poly2[j].y + miny;
allPoints[M * i + j] = new Point(nx, ny);
}
}
//System.err.println(Arrays.toString(allPoints));
//System.err.flush();
return convexHull(allPoints);
}
private Point[] convexHull(Point[] points) {
int pos = 0;
for (int i = 1; i < points.length; ++i)
if (points[i].x < points[pos].x ||
(Math.abs(points[i].x - points[pos].x) < eps &&
points[i].y < points[pos].y)) pos = i;
if (pos != 0) {
Point aux = points[pos];
points[pos] = points[0];
points[0] = aux;
}
final Point ref = points[0];
Arrays.sort(points, 1, points.length, new Comparator<Point>() {
public int compare(Point o1, Point o2) {
double angle1 = slope(ref, o1), angle2 = slope(ref, o2);
if (Math.abs(angle1 - angle2) < eps)
return Double.compare(distSquare(ref, o1), distSquare(ref, o2));
return Double.compare(angle1, angle2);
}
});
Point[] result = new Point[points.length];
int top = 0;
for (Point point : points) {
while (top >= 2 && crossProduct(result[top - 2], result[top - 1], point) < eps)
top--;
result[top++] = point;
}
return Arrays.copyOf(result, top);
}
private boolean checkPoint(Point point, Point[][] polygons) {
for (Point[] poly : polygons)
if (isInside(point, poly))
return false;
return true;
}
private boolean isInside(Point point, Point[] polygon) {
boolean inside = true;
for (int i = 0; i < polygon.length; ++i) {
int next = (i + 1) % polygon.length;
inside &= crossProduct(polygon[i], polygon[next], point) > eps;
}
return inside;
}
private double shortestPath(Point[] points, Point[][] obstacles, int start, int end) {
int N = points.length;
double[] dist = new double[N];
Arrays.fill(dist, 1e99);
dist[start] = 0;
TreeSet<State> orderedNodes = new TreeSet<State>();
orderedNodes.add(new State(start, 0));
graph = new byte[N][N];
badPoint = new boolean[N];
for (int i = 0; i < N; ++i)
badPoint[i] = !checkPoint(points[i], obstacles);
while (!orderedNodes.isEmpty()) {
int node = orderedNodes.first().node;
double cost = orderedNodes.pollFirst().dist;
//if (cost > dist[node]) continue;
if (node == end) return cost;
for (int i = 0; i < N; ++i) {
if (connected(points, obstacles, node, i) &&
dist[i] > dist[node] + dist(points[node], points[i])) {
dist[i] = dist[node] + dist(points[node], points[i]);
orderedNodes.add(new State(i,
dist[i] + dist(points[i], points[end])));
}
}
}
return -1;
}
private boolean connected(Point[] points, Point[][] obstacles, int x, int y) {
if (x > y) {
int aux = x;
x = y;
y = aux;
}
if (graph[x][y] != 0) return graph[x][y] == 1;
if (badPoint[y]) return false;
if (points[x].equals(points[y])) {
graph[x][y] = 1;
return true;
}
if (!checkPoint(points[y], obstacles)) {
graph[x][y] = -1;
return false;
}
for (Point[] obstacle : obstacles) {
if (obstacle.length < 2) continue;
if (intersectsPolygon(points[x], points[y], obstacle)) {
graph[x][y] = -1;
return false;
}
}
graph[x][y] = 1;
return true;
}
private boolean intersectsPolygon(Point a, Point b, Point[] polygon) {
int countTouches = 0;
for (int i = 0; i < polygon.length; ++i) {
Point c = polygon[i], d = polygon[(i + 1) % polygon.length];
if (Math.abs(crossProduct(c, d, a)) < eps &&
Math.abs(crossProduct(c, d, b)) < eps) return false;
if (intersects(a, b, c, d)) return true;
if (onSegment(c, a, b)) countTouches++;
if (crossProduct(a, b, c) * crossProduct(a, b, d) < -eps &&
(onSegment(a, c, d) || onSegment(b, c, d)))
countTouches++;
d = polygon[(i + 2) % polygon.length];
if (intersects(a, b, c, d)) return true;
}
return countTouches > 1;
}
private boolean onSegment(Point o, Point a, Point b) {
return Math.abs(crossProduct(o, a, b)) < eps &&
Math.min(a.x, b.x) < o.x && o.x < Math.max(a.x, b.x) &&
Math.min(a.y, b.y) < o.y && o.y < Math.max(a.y, b.y);
}
private boolean intersects(Point a, Point b, Point c, Point d) {
return (crossProduct(c, d, a) * crossProduct(c, d, b) < -eps) &&
(crossProduct(a, b, c) * crossProduct(a, b, d) < -eps);
}
private class Point {
double x;
double y;
Point(double x, double y) {
this.x = x;
this.y = y;
}
public boolean equals(Object e) {
if (!(e instanceof Point)) return false;
Point other = (Point) e;
return Math.abs(x - other.x) < eps && Math.abs(y - other.y) < eps;
}
public String toString() {
return String.format("{%.2f, %.2f}", x, y);
}
}
private class State implements Comparable<State> {
int node;
double dist;
State(int node, double dist) {
this.node = node;
this.dist = dist;
}
public int compareTo(State other) {
if (Math.abs(dist - other.dist) < eps)
return Integer.compare(node, other.node);
return Double.compare(dist, other.dist);
}
}
}
static class InputReader {
private InputStream stream;
private byte[] buf = new byte[1024];
private int curChar;
private int numChars;
public InputReader(InputStream stream) {
this.stream = stream;
}
public int read() {
if (numChars == -1)
throw new UnknownError();
if (curChar >= numChars) {
curChar = 0;
try {
numChars = stream.read(buf);
} catch (IOException e) {
throw new UnknownError();
}
if (numChars <= 0)
return -1;
}
return buf[curChar++];
}
public int nextInt() {
return Integer.parseInt(next());
}
public String next() {
int c = read();
while (isSpaceChar(c))
c = read();
StringBuffer res = new StringBuffer();
do {
res.appendCodePoint(c);
c = read();
} while (!isSpaceChar(c));
return res.toString();
}
public double nextDouble() {
int c = read();
while (isSpaceChar(c))
c = read();
int sgn = 1;
if (c == '-') {
sgn = -1;
c = read();
}
double res = 0;
while (!isSpaceChar(c) && c != '.') {
if (c == 'e' || c == 'E')
return res * Math.pow(10, nextInt());
if (c < '0' || c > '9')
throw new InputMismatchException();
res *= 10;
res += c - '0';
c = read();
}
if (c == '.') {
c = read();
double m = 1;
while (!isSpaceChar(c)) {
if (c == 'e' || c == 'E')
return res * Math.pow(10, nextInt());
if (c < '0' || c > '9')
throw new InputMismatchException();
m /= 10;
res += (c - '0') * m;
c = read();
}
}
return res * sgn;
}
private boolean isSpaceChar(int c) {
return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
}
}
}