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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            ATwoSquares solver = new ATwoSquares();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class ATwoSquares {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            Rect r1 = new Rect();
            Rect r2 = new Rect();
            for (int i = 0; i < 4; i++) {
                r1.update(in.readInt(), in.readInt());
            }
            for (int i = 0; i < 4; i++) {
                r2.update(in.readInt(), in.readInt());
            }

            for (int x = -100; x <= 100; x++) {
                for (int y = -100; y <= 100; y++) {
                    if (contain1(r1, x, y) && contain2(r2, x, y)) {
                        out.println("YES");
                        return;
                    }
                }
            }
            out.println("NO");
        }

        public boolean contain1(Rect rect, int x, int y) {
            return x >= rect.l && x <= rect.r && y >= rect.b && y <= rect.t;
        }

        public boolean contain2(Rect rect, int x, int y) {
            int cx = (rect.l + rect.r) / 2;
            int cy = (rect.b + rect.t) / 2;
            int dist = Math.abs(cx - x) + Math.abs(cy - y);
            return dist <= cx - rect.l;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 20];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Rect {
        int l = 100;
        int r = -100;
        int t = -100;
        int b = 100;

        public void update(int x, int y) {
            l = Math.min(l, x);
            r = Math.max(r, x);
            t = Math.max(t, y);
            b = Math.min(b, y);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(String c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(String c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }
}

