Problem: Polycarpus likes giving presents to Paraskevi. He has bought two chocolate bars, each of them has the shape of a segmented rectangle. The first bar is a1 × b1 segments large and the second one is a2 × b2 segments large.

Polycarpus wants to give Paraskevi one of the bars at the lunch break and eat the other one himself. Besides, he wants to show that Polycarpus's mind and Paraskevi's beauty are equally matched, so the two bars must have the same number of squares.

To make the bars have the same number of squares, Polycarpus eats a little piece of chocolate each minute. Each minute he does the following:

  * he either breaks one bar exactly in half (vertically or horizontally) and eats exactly a half of the bar, 
  * or he chips of exactly one third of a bar (vertically or horizontally) and eats exactly a third of the bar. 



In the first case he is left with a half, of the bar and in the second case he is left with two thirds of the bar.

Both variants aren't always possible, and sometimes Polycarpus cannot chip off a half nor a third. For example, if the bar is 16 × 23, then Polycarpus can chip off a half, but not a third. If the bar is 20 × 18, then Polycarpus can chip off both a half and a third. If the bar is 5 × 7, then Polycarpus cannot chip off a half nor a third.

What is the minimum number of minutes Polycarpus needs to make two bars consist of the same number of squares? Find not only the required minimum number of minutes, but also the possible sizes of the bars after the process.

Input

The first line of the input contains integers a1, b1 (1 ≤ a1, b1 ≤ 109) — the initial sizes of the first chocolate bar. The second line of the input contains integers a2, b2 (1 ≤ a2, b2 ≤ 109) — the initial sizes of the second bar.

You can use the data of type int64 (in Pascal), long long (in С++), long (in Java) to process large integers (exceeding 231 - 1).

Output

In the first line print m — the sought minimum number of minutes. In the second and third line print the possible sizes of the bars after they are leveled in m minutes. Print the sizes using the format identical to the input format. Print the sizes (the numbers in the printed pairs) in any order. The second line must correspond to the first bar and the third line must correspond to the second bar. If there are multiple solutions, print any of them.

If there is no solution, print a single line with integer -1.

Examples

Input

2 6
2 3


Output

1
1 6
2 3


Input

36 5
10 16


Output

3
16 5
5 16


Input

3 5
2 1


Output

-1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.util.Collection;
import java.util.InputMismatchException;
import java.util.HashMap;
import java.io.IOException;
import java.io.FileInputStream;
import java.util.ArrayList;
import java.util.HashSet;
import java.util.Objects;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Queue;
import java.util.LinkedList;
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 = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        DChocolate solver = new DChocolate();
        solver.solve(1, in, out);
        out.close();
    }

    static class DChocolate {
        private HashMap<Long, Util.Triplet<Long>> hm = new HashMap<>();
        private HashMap<Long, Util.Triplet<Long>> hm2 = new HashMap<>();
        private HashSet<Util.Pair<Long>> hs = new HashSet<>();
        long minDis = Integer.MAX_VALUE;
        private Util.Pair<Long> pair1;
        private Util.Pair<Long> pair2;

        private void bfs(long x, long y, OutputWriter out) {
            long area = x * y;
            hm.put(area, new Util.Triplet<>(0L, x, y));
            Queue<Util.Pair<Long>> queue = new LinkedList<>();
            queue.offer(new Util.Pair<>(x, y));
            hs.add(new Util.Pair<>(x, y));
            while (!queue.isEmpty()) {
                Util.Pair<Long> P = queue.poll();
//            out.println(P.toString());
                long area1;
                long distance = hm.get(P.x * P.y).x;
                if (P.x % 2 == 0 && !hs.contains(new Util.Pair<>(P.x / 2, P.y))) {
                    area1 = P.y * P.x / 2;

                    queue.offer(new Util.Pair<>((P.x) / 2, P.y));
                    if (hm.containsKey(area1)) {
                        long dis = hm.get(area1).x;
                        if (distance + 1 < dis) {
                            hm.put(area1, new Util.Triplet<>(distance + 1, P.x / 2, P.y));
                        }
                    } else hm.put(area1, new Util.Triplet<>(distance + 1, P.x / 2, P.y));


                    hs.add(new Util.Pair<>(P.x / 2, P.y));
                }
                if (P.y % 2 == 0 && !hs.contains(new Util.Pair<>(P.x, P.y / 2))) {
                    area1 = P.x * P.y / 2;
                    queue.offer(new Util.Pair<>(P.x, P.y / 2));
                    if (hm.containsKey(area1)) {
                        long dis = hm.get(area1).x;
                        if (distance + 1 < dis) {
                            hm.put(area1, new Util.Triplet<>(distance + 1, P.x, P.y / 2));
                        }
                    } else hm.put(area1, new Util.Triplet<>(distance + 1, P.x, P.y / 2));
                    hs.add(new Util.Pair<>(P.x, P.y / 2));
                }
                if (P.x % 3 == 0 && !hs.contains(new Util.Pair<>(2 * P.x / 3, P.y))) {
                    area1 = 2 * P.y * P.x / 3;
                    queue.offer(new Util.Pair<>(2 * (P.x) / 3, P.y));
                    if (hm.containsKey(area1)) {
                        long dis = hm.get(area1).x;
                        if (distance + 1 < dis) {
                            hm.put(area1, new Util.Triplet<>(distance + 1, 2 * P.x / 3, P.y));
                        }
                    } else hm.put(area1, new Util.Triplet<>(distance + 1, 2 * P.x / 3, P.y));

                    hs.add(new Util.Pair<>(2 * P.x / 3, P.y));
                }
                if (P.y % 3 == 0 && !hs.contains(new Util.Pair<>(P.x, 2 * P.y / 3))) {
                    area1 = 2 * P.x * P.y / 3;
                    queue.offer(new Util.Pair<>(P.x, 2 * P.y / 3));
                    if (hm.containsKey(area1)) {
                        long dis = hm.get(area1).x;
                        if (distance + 1 < dis) {
                            hm.put(area1, new Util.Triplet<>(distance + 1, P.x, 2 * P.y / 3));
                        }
                    } else hm.put(area1, new Util.Triplet<>(distance + 1, P.x, 2 * P.y / 3));

                    hs.add(new Util.Pair<>(P.x, 2 * P.y / 3));
                }
            }
        }

        private void bfs2(long x, long y) {
            long area = x * y;
            hm2.put(area, new Util.Triplet<>(0L, x, y));
            if (hm.containsKey(area)) {
                if (minDis > hm.get(area).x + hm2.get(area).x) {
                    minDis = hm.get(area).x + hm2.get(area).x;
                    pair1 = new Util.Pair<>(hm.get(area).y, hm.get(area).z);
                    pair2 = new Util.Pair<>(x, y);
                }
            }
            Queue<Util.Pair<Long>> queue = new LinkedList<>();
            queue.offer(new Util.Pair<>(x, y));
            hs.add(new Util.Pair<>(x, y));
            while (!queue.isEmpty()) {
                Util.Pair<Long> P = queue.poll();
                long area1;
                long distance = hm2.get(P.x * P.y).x;
                if (P.x % 2 == 0 && !hs.contains(new Util.Pair<>(P.x / 2, P.y))) {
                    area1 = P.y * P.x / 2;
                    queue.offer(new Util.Pair<>((P.x) >> 1, P.y));
                    if (hm2.containsKey(area1)) {
                        long dis = hm2.get(area1).x;
                        if (distance + 1 < dis) {
                            hm2.put(area1, new Util.Triplet<>(distance + 1, P.x / 2, P.y));
                        }
                    } else hm2.put(area1, new Util.Triplet<>(distance + 1, P.x / 2, P.y));
                    if (hm.containsKey(area1)) {
                        if (minDis > hm.get(area1).x + hm2.get(area1).x) {
                            minDis = hm.get(area1).x + hm2.get(area1).x;
                            pair1 = new Util.Pair<>(hm.get(area1).y, hm.get(area1).z);
                            pair2 = new Util.Pair<>(P.x / 2, P.y);
                        }
                    }
                    hs.add(new Util.Pair<>(P.x / 2, P.y));

                }
                if (P.y % 2 == 0 && !hs.contains(new Util.Pair<>(P.x, P.y / 2))) {
                    area1 = P.x * P.y / 2;
                    queue.offer(new Util.Pair<>(P.x, P.y / 2));
                    if (hm2.containsKey(area1)) {
                        long dis = hm2.get(area1).x;
                        if (distance + 1 < dis) {
                            hm2.put(area1, new Util.Triplet<>(distance + 1, P.x, P.y / 2));
                        }
                    } else hm2.put(area1, new Util.Triplet<>(distance + 1, P.x, P.y / 2));
                    if (hm.containsKey(area1)) {
                        if (minDis > hm.get(area1).x + hm2.get(area1).x) {
                            minDis = hm.get(area1).x + hm2.get(area1).x;
                            pair1 = new Util.Pair<>(hm.get(area1).y, hm.get(area1).z);
                            pair2 = new Util.Pair<>(P.x, P.y / 2);
                        }
                    }
                    hs.add(new Util.Pair<>(P.x, P.y / 2));
                }
                if (P.x % 3 == 0 && !hs.contains(new Util.Pair<>(2 * P.x / 3, P.y))) {
                    area1 = 2 * P.y * P.x / 3;
                    queue.offer(new Util.Pair<>(2 * (P.x) / 3, P.y));
                    if (hm2.containsKey(area1)) {
                        long dis = hm2.get(area1).x;
                        if (distance + 1 < dis) {
                            hm2.put(area1, new Util.Triplet<>(distance + 1, 2 * P.x / 3, P.y));
                        }
                    } else hm2.put(area1, new Util.Triplet<>(distance + 1, 2 * P.x / 3, P.y));
                    if (hm.containsKey(area1)) {
                        if (minDis > hm.get(area1).x + hm2.get(area1).x) {
                            minDis = hm.get(area1).x + hm2.get(area1).x;
                            pair1 = new Util.Pair<>(hm.get(area1).y, hm.get(area1).z);
                            pair2 = new Util.Pair<>(2 * P.x / 3, P.y);
                        }
                    }
                    hs.add(new Util.Pair<>(2 * P.x / 3, P.y));
                }
                if (P.y % 3 == 0 && !hs.contains(new Util.Pair<>(P.x, 2 * P.y / 3))) {
                    area1 = 2 * P.x * P.y / 3;
                    queue.offer(new Util.Pair<>(P.x, 2 * P.y / 3));
                    if (hm2.containsKey(area1)) {
                        long dis = hm2.get(area1).x;
                        if (distance + 1 < dis) {
                            hm2.put(area1, new Util.Triplet<>(distance + 1, P.x, 2 * P.y / 3));
                        }
                    } else hm2.put(area1, new Util.Triplet<>(distance + 1, P.x, 2 * P.y / 3));
                    if (hm.containsKey(area1)) {
                        if (minDis > hm.get(area1).x + hm2.get(area1).x) {
                            minDis = hm.get(area1).x + hm2.get(area1).x;
                            pair1 = new Util.Pair<>(hm.get(area1).y, hm.get(area1).z);
                            pair2 = new Util.Pair<>(P.x, 2 * P.y / 3);
                        }
                    }
                    hs.add(new Util.Pair<>(P.x, 2 * P.y / 3));
                }
            }
        }

        public void solve(int testNumber, InputReader in, OutputWriter out) {
            long a1 = in.nextLong(), b1 = in.nextLong();
            long a2 = in.nextLong(), b2 = in.nextLong();
            bfs(a1, b1, out);
            hs.clear();
            bfs2(a2, b2);
//        out.println(hm.toString());
//        out.println(hm2.toString());
            if (minDis == Integer.MAX_VALUE) out.println(-1);
            else {
                out.println(minDis);
                out.printsc(pair1.x, pair1.y);
                out.println();
                out.printsc(pair2.x, pair2.y);
                out.println();
            }


            out.flush();
        }

    }

    static class Util {
        public static class Pair<T> {
            public T x;
            public T y;

            public Pair(T x, T y) {
                this.x = x;
                this.y = y;
            }

            public boolean equals(Object obj) {
                if (!(obj instanceof Util.Pair)) return false;
                Util.Pair<T> pair = (Util.Pair<T>) obj;
                return this.x.equals(pair.x) && this.y.equals(pair.y);
            }

            public String toString() {
                return ("(" + this.x + "," + this.y + ")");
            }

            public int hashCode() {
                return Objects.hash(x, y);
            }

        }

        public static class Triplet<T> {
            public T x;
            public T y;
            public T z;

            public Triplet(T x, T y, T z) {
                this.x = x;
                this.y = y;
                this.z = z;
            }

            public boolean equals(Object obj) {
                if (!(obj instanceof Util.Triplet)) return false;
                Util.Triplet<T> triplet = (Util.Triplet<T>) obj;
                return this.x.equals(triplet.x) && this.y.equals(triplet.y) && this.z.equals(triplet.z);
            }

            public String toString() {
                return ("(" + this.x + "," + this.y + "," + this.z + ")");
            }

            public int hashCode() {
                return Objects.hash(x, y, z);
            }

        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public InputReader(FileInputStream file) {
            this.stream = file;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res = (res << 3) + (res << 1) + c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

    }

    static class OutputWriter {
        private final PrintWriter writer;
        private ArrayList<String> res = new ArrayList<>();
        private StringBuilder sb = new StringBuilder("");

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void println(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]);
            }
            res.add(sb.toString());
            sb = new StringBuilder("");
        }

        public void printsc(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                sb.append(objects[i]).append(' ');
            }
        }

        public void close() {
            writer.close();
        }

        public void flush() {
            for (String str : res) writer.printf("%s\n", str);
            res.clear();
            sb = new StringBuilder("");
        }

    }
}