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.io.PrintWriter;
import java.util.Iterator;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.FileNotFoundException;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.BufferedReader;
import java.util.LinkedList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Asgar Javadov
 */
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);
        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, InputReader in, OutputWriter out) {
            int n = in.nextInt();

            List<IntPair> primeFactors = NumberTheory.primeFactorization(n);
            LinkedList<Integer> list = new LinkedList<>();
            for (int i = primeFactors.size() - 1; i >= 0; --i) {
                int current = primeFactors.get(i).first;
                int next = (i < primeFactors.size() - 1) ? primeFactors.get(i + 1).first : -1;
                LinkedList<Integer> currentList = new LinkedList<>();
                if (next != -1) {
                    int product = current * next;
                    if (product < n) {
                        currentList.add(product);
                    }
                }

                for (int e : list) {
                    for (int j = 1, currentPower = 1; j <= primeFactors.get(i).second; ++j) {
                        currentPower *= current;
                        if (e == next && j == 1) continue;
                        int product = e * currentPower;
                        if (product < n) {
                            currentList.add(product);
                        }
                    }
                }
                for (int j = 1, currentPower = 1; j <= primeFactors.get(i).second; ++j) {
                    currentPower *= current;
                    if (currentPower < n) {
                        currentList.add(currentPower);
                    }
                }
                list.addAll(currentList);
            }
            list.addFirst(n);

            out.println(list);
            if (primeFactors.size() == 2 && primeFactors.get(0).second == 1 && primeFactors.get(1).second == 1) {
                out.one();
            } else {
                out.zero();
            }
        }

    }

    static class NumberTheory {
        public static List<IntPair> primeFactorization(int n) {
            List<IntPair> result = new ArrayList<>();

            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) {
                    IntPair pair = IntPair.of(i, 0);

                    while (n % i == 0) {
                        pair.second++;
                        n /= i;
                    }

                    result.add(pair);
                }
            }

            if (n > 1) {
                result.add(IntPair.of(n, 1));
            }

            return result;
        }

    }

    static class OutputWriter extends PrintWriter {
        public OutputWriter(OutputStream outputStream) {
            super(outputStream);
        }

        public OutputWriter(Writer writer) {
            super(writer);
        }

        public OutputWriter(String filename) throws FileNotFoundException {
            super(filename);
        }

        public void println(Iterable<?> collection) {
            Iterator<?> iter = collection.iterator();

            if (iter.hasNext())
                print(iter.next());
            while (iter.hasNext()) {
                print(' ');
                print(iter.next());
            }
            println();
        }

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

        public void zero() {
            println(0);
        }

        public void one() {
            println(1);
        }

    }

    static class IntPair implements Comparable<IntPair> {
        public int first;
        public int second;

        public IntPair(int first, int second) {
            this.first = first;
            this.second = second;
        }

        public int compareTo(IntPair o) {
            if (first != o.first)
                return Integer.compare(first, o.first);
            return Integer.compare(second, o.second);
        }

        public String toString() {
            return first + " " + second;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof IntPair)) return false;
            IntPair intPair = (IntPair) o;
            return first == intPair.first &&
                    second == intPair.second;
        }

        public int hashCode() {
            return (31 * first + second);
        }

        public IntPair clone() {
            return of(first, second);
        }

        public static IntPair of(int first, int second) {
            return new IntPair(first, second);
        }

    }

    static class InputReader extends BufferedReader {
        StringTokenizer tokenizer;

        public InputReader(InputStream inputStream) {
            super(new InputStreamReader(inputStream), 32768);
        }

        public InputReader(String filename) {
            super(new InputStreamReader(Thread.currentThread().getContextClassLoader().getResourceAsStream(filename)));
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String line = readLine();
                    if (line == null) continue;
                    tokenizer = new StringTokenizer(line);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
            }
            return tokenizer.nextToken();
        }

        public Integer nextInt() {
            return Integer.valueOf(next());
        }

    }
}