Problem: The Squareland national forest is divided into equal 1 × 1 square plots aligned with north-south and east-west directions. Each plot can be uniquely described by integer Cartesian coordinates (x, y) of its south-west corner.

Three friends, Alice, Bob, and Charlie are going to buy three distinct plots of land A, B, C in the forest. Initially, all plots in the forest (including the plots A, B, C) are covered by trees. The friends want to visit each other, so they want to clean some of the plots from trees. After cleaning, one should be able to reach any of the plots A, B, C from any other one of those by moving through adjacent cleared plots. Two plots are adjacent if they share a side.

<image> For example, A=(0,0), B=(1,1), C=(2,2). The minimal number of plots to be cleared is 5. One of the ways to do it is shown with the gray color.

Of course, the friends don't want to strain too much. Help them find out the smallest number of plots they need to clean from trees.

Input

The first line contains two integers x_A and y_A — coordinates of the plot A (0 ≤ x_A, y_A ≤ 1000). The following two lines describe coordinates (x_B, y_B) and (x_C, y_C) of plots B and C respectively in the same format (0 ≤ x_B, y_B, x_C, y_C ≤ 1000). It is guaranteed that all three plots are distinct.

Output

On the first line print a single integer k — the smallest number of plots needed to be cleaned from trees. The following k lines should contain coordinates of all plots needed to be cleaned. All k plots should be distinct. You can output the plots in any order.

If there are multiple solutions, print any of them.

Examples

Input


0 0
1 1
2 2


Output


5
0 0
1 0
1 1
1 2
2 2


Input


0 0
2 0
1 1


Output


4
0 0
1 0
1 1
2 0

Note

The first example is shown on the picture in the legend.

The second example is illustrated with the following image:

<image>

Solution (in JAVA):

Solution:


import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.nio.charset.Charset;
import java.util.Arrays;
import java.util.Comparator;

public class CT1086A {
    public static void main(String[] args) throws Exception {
        boolean local = System.getProperty("ONLINE_JUDGE") == null;
        boolean async = false;

        Charset charset = Charset.forName("ascii");

        FastIO io = local ? new FastIO(new FileInputStream("D:\\database\\testcase\\code.in"), System.out, charset) : new FastIO(System.in, System.out, charset);
        Task task = new Task(io, new Debug(local));

        if (async) {
            Thread t = new Thread(null, task, "dalt", 1 << 27);
            t.setPriority(Thread.MAX_PRIORITY);
            t.start();
            t.join();
        } else {
            task.run();
        }

        if (local) {
            io.cache.append("\n\n--memory -- \n" + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");
        }

        io.flush();
    }

    public static class Task implements Runnable {
        final FastIO io;
        final Debug debug;
        int inf = (int) 1e8;

        public Task(FastIO io, Debug debug) {
            this.io = io;
            this.debug = debug;
        }

        @Override
        public void run() {
            solve();
        }

        public void solve() {
            int[][] points = new int[3][2];
            for (int i = 0; i < 3; i++) {
                for (int j = 0; j < 2; j++) {
                    points[i][j] = io.readInt();
                }
            }

            int min = inf;
            int[] center = new int[2];
            for (int i = 0; i <= 1000; i++) {
                for (int j = 0; j <= 1000; j++) {
                    int distance = 0;
                    for (int k = 0; k < 3; k++) {
                        distance += Math.max(0, Math.abs(points[k][0] - i) + Math.abs(points[k][1] - j) - 1);
                    }
                    if (!(equal(i, j, points[0])
                            || equal(i, j, points[1])
                            || equal(i, j, points[2]))) {
                        distance++;
                    }
                    if (min > distance) {
                        min = distance;
                        center[0] = i;
                        center[1] = j;
                    }
                }
            }

            io.cache.append(min + 3).append('\n');
            io.cache.append(center[0]).append(' ').append(center[1]).append('\n');


            for (int i = 0; i < 3; i++) {
                displayPathBetween(center, points[i]);
            }
        }

        public boolean equal(int[] a, int[] b) {
            return a[0] == b[0] && a[1] == b[1];
        }

        public boolean equal(int ay, int ax, int[] b) {
            return ay == b[0] && ax == b[1];
        }

        public void displayPathBetween(int[] from, int[] to) {
            int y = from[0];
            int x = from[1];
            while (y != to[0]) {
                if (y < to[0]) {
                    y++;
                } else {
                    y--;
                }
                io.cache.append(y).append(' ').append(x).append('\n');
            }
            while (x != to[1]) {
                if (x < to[1]) {
                    x++;
                } else {
                    x--;
                }
                io.cache.append(y).append(' ').append(x).append('\n');
            }
        }
    }

    public static class FastIO {
        private final InputStream is;
        private final OutputStream os;
        private final Charset charset;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 8);
        public final StringBuilder cache = new StringBuilder();

        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastIO(InputStream is, OutputStream os, Charset charset) {
            this.is = is;
            this.os = os;
            this.charset = charset;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                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;
        }

        public long readLong() {
            int sign = 1;

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

            long 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;
        }

        public double readDouble() {
            long num = readLong();
            if (next != '.') {
                return num;
            }

            next = read();
            long divisor = 1;
            long later = 0;
            while (next >= '0' && next <= '9') {
                divisor = divisor * 10;
                later = later * 10 + next - '0';
                next = read();
            }

            if (num >= 0) {
                return num + (later / (double) divisor);
            } else {
                return num - (later / (double) divisor);
            }
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public int readString(byte[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (byte) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public void flush() {
            try {
                os.write(cache.toString().getBytes(charset));
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public boolean hasMore() {
            skipBlank();
            return next != -1;
        }
    }

    public static class Memory {
        public static <T> void swap(T[] data, int i, int j) {
            T tmp = data[i];
            data[i] = data[j];
            data[j] = tmp;
        }

        public static <T> int min(T[] data, int from, int to, Comparator<T> cmp) {
            int m = from;
            for (int i = from + 1; i < to; i++) {
                if (cmp.compare(data[m], data[i]) > 0) {
                    m = i;
                }
            }
            return m;
        }

        public static <T> void move(T[] data, int from, int to, int step) {
            int len = to - from;
            step = len - (step % len + len) % len;
            Object[] buf = new Object[len];
            for (int i = 0; i < len; i++) {
                buf[i] = data[(i + step) % len + from];
            }
            System.arraycopy(buf, 0, data, from, len);
        }

        public static <T> void reverse(T[] data, int f, int t) {
            int l = f, r = t - 1;
            while (l < r) {
                swap(data, l, r);
                l++;
                r--;
            }
        }

        public static void copy(Object[] src, Object[] dst, int srcf, int dstf, int len) {
            if (len < 8) {
                for (int i = 0; i < len; i++) {
                    dst[dstf + i] = src[srcf + i];
                }
            } else {
                System.arraycopy(src, srcf, dst, dstf, len);
            }
        }
    }

    public static class Debug {
        private boolean allowDebug;

        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }

        private void outputName(String name) {
            System.out.print(name + " = ");
        }

        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }

            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}