Problem: An agent called Cypher is decrypting a message, that contains a [composite number](https://en.wikipedia.org/wiki/Composite_number) n. All divisors of n, which are greater than 1, are placed in a circle. Cypher can choose the initial order of numbers in the circle.

In one move Cypher can choose two adjacent numbers in a circle and insert their [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) between them. He can do that move as many times as needed.

A message is decrypted, if every two adjacent numbers are not coprime. Note that for such constraints it's always possible to decrypt the message.

Find the minimal number of moves that Cypher should do to decrypt the message, and show the initial order of numbers in the circle for that.

Input

The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases. Next t lines describe each test case.

In a single line of each test case description, there is a single composite number n (4 ≤ n ≤ 10^9) — the number from the message.

It's guaranteed that the total number of divisors of n for all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case in the first line output the initial order of divisors, which are greater than 1, in the circle. In the second line output, the minimal number of moves needed to decrypt the message.

If there are different possible orders with a correct answer, print any of them.

Example

Input


3
6
4
30


Output


2 3 6 
1
2 4 
0
2 30 6 3 15 5 10 
0

Note

In the first test case 6 has three divisors, which are greater than 1: 2, 3, 6. Regardless of the initial order, numbers 2 and 3 are adjacent, so it's needed to place their least common multiple between them. After that the circle becomes 2, 6, 3, 6, and every two adjacent numbers are not coprime.

In the second test case 4 has two divisors greater than 1: 2, 4, and they are not coprime, so any initial order is correct, and it's not needed to place any least common multiples.

In the third test case all divisors of 30 greater than 1 can be placed in some order so that there are no two adjacent numbers that are coprime.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Set;
import java.io.IOException;
import java.util.ArrayList;
import java.util.HashSet;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Collections;
import java.io.InputStream;

/**
 * @author khokharnikunj8
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "khokharnikunj8", 1 << 29);
        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);
            EDecryption solver = new EDecryption();
            int testCount = Integer.parseInt(in.next());
            for (int i = 1; i <= testCount; i++)
                solver.solve(i, in, out);
            out.close();
        }
    }

    static class EDecryption {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            List<Integer> divisors = new ArrayList<>();
            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) {
                    divisors.add(i);
                    if (i != n / i) divisors.add(n / i);
                }
            }
            divisors.add(n);
            Collections.sort(divisors);
            List<Integer> primes = new ArrayList<>();
            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) {
                    while (n % i == 0) n /= i;
                    primes.add(i);
                }
            }
            if (n > 1) primes.add(n);
            if (divisors.size() == 3 && divisors.get(0) * divisors.get(1) == divisors.get(2) && primes.size() == 2) {
                for (int i : divisors) out.append(i + " ");
                out.println();
                out.println(1);
                return;
            }
            Set<Integer> setDivisors = new HashSet<>(divisors);
            if (primes.size() == 2) {
                setDivisors.remove(primes.get(0) * primes.get(1));

                int which = -1;
                for (int i : setDivisors) if (i % primes.get(0) == 0 && i % primes.get(1) == 0) which = i;
                setDivisors.remove(which);


                setDivisors.remove(primes.get(0));
                out.append(primes.get(0) + " ");

                List<Integer> toRemove = new ArrayList<>();
                for (int i : setDivisors) if (i % primes.get(0) == 0) toRemove.add(i);
                for (int i : toRemove) {
                    out.append(i + " ");
                    setDivisors.remove(i);
                }

                out.append(primes.get(0) * primes.get(1) + " ");


                out.append(primes.get(1) + " ");
                setDivisors.remove(primes.get(1));


                for (int i : setDivisors) out.append(i + " ");

                out.append(which + " ");
                out.println();
                out.println(0);
                return;


            }
            if (primes.size() == 1) {
                for (int i : divisors) out.append(i + " ");
                out.println();
                out.println(0);
                return;
            }

            for (int i = 0; i < primes.size(); i++) {
                setDivisors.remove(primes.get(i));
                setDivisors.remove(primes.get(i) * primes.get((i + 1) % primes.size()));
            }
            for (int i = 0; i < primes.size(); i++) {
                out.append(primes.get(i) + " ");
                List<Integer> toRemove = new ArrayList<>();
                for (int j : setDivisors) {
                    if (j % primes.get(i) == 0)
                        toRemove.add(j);
                }
                for (int j : toRemove) {
                    out.append(j + " ");
                    setDivisors.remove(j);
                }
                out.append((primes.get(i) * primes.get((i + 1) % primes.size())) + " ");
            }
            out.println();
            out.println(0);
        }

    }

    static class FastInput {
        private final InputStream is;
        private final StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private final byte[] buf = new byte[1 << 13];
        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 String next() {
            return readString();
        }

        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 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);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private final Writer os;
        private final StringBuilder cache = new StringBuilder(5 << 20);

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

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(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 append(char c) {
            cache.append(c);
            return this;
        }

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

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

        public FastOutput println(int 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();
        }

    }
}