You are given two squares, one with sides parallel to the coordinate axes, and another one with sides at 45 degrees to the coordinate axes. Find whether the two squares intersect.

The interior of the square is considered to be part of the square, i.e. if one square is completely inside another, they intersect. If the two squares only share one common point, they are also considered to intersect.

Input

The input data consists of two lines, one for each square, both containing 4 pairs of integers. Each pair represents coordinates of one vertex of the square. Coordinates within each line are either in clockwise or counterclockwise order.

The first line contains the coordinates of the square with sides parallel to the coordinate axes, the second line contains the coordinates of the square at 45 degrees.

All the values are integer and between -100 and 100.

Output

Print "Yes" if squares intersect, otherwise print "No".

You can print each letter in any case (upper or lower).

Examples

Input

0 0 6 0 6 6 0 6
1 3 3 5 5 3 3 1


Output

YES


Input

0 0 6 0 6 6 0 6
7 3 9 5 11 3 9 1


Output

NO


Input

6 0 6 6 0 6 0 0
7 4 4 7 7 10 10 7


Output

YES

Note

In the first example the second square lies entirely within the first square, so they do intersect.

In the second sample squares do not have any points in common.

Here are images corresponding to the samples:

<image> <image> <image>
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 *
 * @author pttrung
 */
public class A_Round_488_Div1 {

    public static long MOD = 998244353;
    static long[][][] dp;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        Point[] a = new Point[4];
        Point[] b = new Point[4];
        for (int i = 0; i < 4; i++) {
            a[i] = new Point(in.nextInt(), in.nextInt());
        }
        for (int i = 0; i < 4; i++) {
            b[i] = new Point(in.nextInt(), in.nextInt());
        }

        boolean ok = false;
        for (Point x : a) {
            for (Point y : b) {
                ok |= x.equals(y);
            }
        }
        for (int i = 0; i < 4; i++) {
            ok |= isInside(a[i], b);
            ok |= isInside(b[i], a);
        }
        for (int i = 0; i < 4; i++) {
            int x = (i + 1) % 4;
            for (int j = 0; j < 4; j++) {
                int y = (j + 1) % 4;
                ok |= isIntersect(a[i], a[x], b[j], b[y]);
            }
        }
        if (ok) {
            out.println("YES");
        } else {
            out.println("NO");
        }
        out.close();
    }

    static boolean isIntersect(Point A, Point B, Point C, Point D) {
        return ccw(A, C, D) != ccw(B, C, D) && ccw(A, B, C) != ccw(A, B, D);
    }

    static boolean ccw(Point A, Point B, Point C) {
        return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x);
    }

    static boolean isInside(Point p, Point[] s) {
        double total = 0;
        for (int i = 0; i < 4; i++) {
            int nxt = (i + 1) % 4;
            Point x = new Point(s[i].x - p.x, s[i].y - p.y);
            Point y = new Point(s[nxt].x - p.x, s[nxt].y - p.y);
            total += angle(x, y);
            // System.out.println(Math.toDegrees(angle(x, y)));
        }
        //System.out.println(p + " " + Arrays.toString(s) + " " + total + " " + 2 * Math.PI);
        return Math.abs(total - 2 * Math.PI) < 1e-6;
    }

    static double angle(Point a, Point b) {
        double dot = a.x * b.x + a.y * b.y;
        double A = a.x * a.x + a.y * a.y;
        A = Math.sqrt(A);
        double B = b.x * b.x + b.y * b.y;
        B = Math.sqrt(B);
        double angle = dot / (A * B);
        return Math.acos(angle);
    }


    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        public String toString() {
            return x + " : " + y;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}