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.BufferedOutputStream;
import java.io.Closeable;
import java.io.DataInputStream;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.LinkedHashSet;
import java.util.Objects;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			long startTime = System.currentTimeMillis();
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			FastReader in = new FastReader(inputStream);
			Output out = new Output(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();
			System.err.println(System.currentTimeMillis()-startTime+"ms");
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<28);
		thread.start();
		thread.join();
	}

	static class EDecryption {
		ArrayList<Integer> primes = Utilities.sieve(31623);

		public EDecryption() {
		}

		public ArrayList<Long> factors(ArrayList<Pair<Long, Integer>> x) {
			ArrayList<Long> ret = new ArrayList<>();
			findAll(0, 1, x, ret);
			return ret;
		}

		private void findAll(int ind, long cur, ArrayList<Pair<Long, Integer>> factor, ArrayList<Long> ret) {
			if(ind==factor.size()) {
				if(cur!=1) {
					ret.add(cur);
				}
				return;
			}
			for(int i = 0; i<=factor.get(ind).b; i++) {
				findAll(ind+1, cur, factor, ret);
				cur *= factor.get(ind).a;
			}
		}

		public void solve(int kase, InputReader in, Output pw) {
			int n = in.nextInt();
			ArrayList<Pair<Long, Integer>> factors = new ArrayList<>();
			for(long i: primes) {
				int cnt = 0;
				while(n%i==0) {
					n /= i;
					cnt++;
				}
				if(cnt>0) {
					factors.add(new Pair<>(i, cnt));
				}
			}
			if(n!=1) {
				factors.add(new Pair<>((long) n, 1));
			}
			ArrayList<Long> divs = factors(factors);
			Utilities.Debug.dbg(factors, divs);
			if(factors.size()==1) {
				pw.println(divs);
				pw.println(0);
				return;
			}else if(factors.size()==2) {
				var a = factors.get(0);
				var b = factors.get(1);
				if(a.b==1&&b.b==1) {
					pw.println(divs);
					pw.println(1);
					return;
				}
				ArrayDeque<Long> x = new ArrayDeque<>(), y = new ArrayDeque<>();
				long times1 = a.a*b.a, times2;
				if(a.b>1) {
					times2 = times1*a.a;
				}else {
					times2 = times1*b.a;
				}
				for(long i: divs) {
					if(i!=times1&&i!=times2) {
						if(i%a.a==0) {
							x.addLast(i);
						}else {
							y.addLast(i);
						}
					}
				}
				pw.print(times1+" ");
				pw.print(x);
				pw.print(" "+times2+" ");
				pw.println(y);
				pw.println(0);
			}else {
				LinkedHashSet<Long> times = new LinkedHashSet<>();
				n = factors.size();
				times.add(factors.get(0).a*factors.get(n-1).a);
				for(int i = 0; i<n-1; i++) {
					times.add(factors.get(i).a*factors.get(i+1).a);
				}
				ArrayDeque<Long>[] list = new ArrayDeque[n];
				for(int i = 0; i<n; i++) {
					list[i] = new ArrayDeque<>();
				}
				for(long i: divs) {
					if(!times.contains(i)) {
						for(int j = 0; j<n; j++) {
							if(i%factors.get(j).a==0) {
								list[j].add(i);
								break;
							}
						}
					}
				}
				Iterator<Long> iter = times.iterator();
				for(int i = 0; i<n; i++) {
					pw.print(iter.next()+" ");
					pw.print(list[i]);
					pw.print(" ");
				}
				pw.println("\n0");
			}
		}

	}

	static class Pair<T1, T2> implements Comparable<Pair<T1, T2>> {
		public T1 a;
		public T2 b;

		public Pair(Pair<T1, T2> p) {
			this(p.a, p.b);
		}

		public Pair(T1 a, T2 b) {
			this.a = a;
			this.b = b;
		}

		public String toString() {
			return a+" "+b;
		}

		public int hashCode() {
			return Objects.hash(a, b);
		}

		public boolean equals(Object o) {
			if(o instanceof Pair) {
				Pair p = (Pair) o;
				return a.equals(p.a)&&b.equals(p.b);
			}
			return false;
		}

		public int compareTo(Pair<T1, T2> p) {
			int cmp = ((Comparable<T1>) a).compareTo(p.a);
			if(cmp==0) {
				return ((Comparable<T2>) b).compareTo(p.b);
			}
			return cmp;
		}

	}

	static class FastReader implements InputReader {
		final private int BUFFER_SIZE = 1<<16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer;
		private int bytesRead;

		public FastReader(InputStream is) {
			din = new DataInputStream(is);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String next() {
			StringBuilder ret = new StringBuilder(64);
			byte c = skip();
			while(c!=-1&&!isSpaceChar(c)) {
				ret.appendCodePoint(c);
				c = read();
			}
			return ret.toString();
		}

		public int nextInt() {
			int ret = 0;
			byte c = skipToDigit();
			boolean neg = (c=='-');
			if(neg) {
				c = read();
			}
			do {
				ret = ret*10+c-'0';
			} while((c = read())>='0'&&c<='9');
			if(neg) {
				return -ret;
			}
			return ret;
		}

		private boolean isSpaceChar(byte b) {
			return b==' '||b=='\r'||b=='\n'||b=='\t'||b=='\f';
		}

		private byte skip() {
			byte ret;
			while(isSpaceChar((ret = read()))) ;
			return ret;
		}

		private boolean isDigit(byte b) {
			return b>='0'&&b<='9';
		}

		private byte skipToDigit() {
			byte ret;
			while(!isDigit(ret = read())&&ret!='-') ;
			return ret;
		}

		private void fillBuffer() {
			try {
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			}catch(IOException e) {
				e.printStackTrace();
				throw new InputMismatchException();
			}
			if(bytesRead==-1) {
				buffer[0] = -1;
			}
		}

		private byte read() {
			if(bytesRead==-1) {
				throw new InputMismatchException();
			}else if(bufferPointer==bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public String lineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			lineSeparator = System.lineSeparator();
		}

		public void print(Object... o) {
			for(int i = 0; i<o.length; i++) {
				if(i!=0) {
					print(" ");
				}
				print(String.valueOf(o[i]));
			}
		}

		public void print(String s) {
			sb.append(s);
			if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println(int i) {
			println(String.valueOf(i));
		}

		public void println(String s) {
			sb.append(s);
			println();
			if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println() {
			sb.append(lineSeparator);
		}

		public <T> void print(Iterable<T> iter) {
			boolean first = true;
			for(T t: iter) {
				if(!first) {
					print(" ");
				}
				first = false;
				print(t);
			}
		}

		public <T> void println(Iterable<T> iter) {
			boolean first = true;
			for(T t: iter) {
				if(!first) {
					print(" ");
				}
				first = false;
				print(t);
			}
			println();
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}

	static interface InputReader {
		int nextInt();

	}

	static class Utilities {
		public static ArrayList<Integer> sieve(int n) {
			ArrayList<Integer> ans = new ArrayList<>();
			boolean[] prime = new boolean[n+1];
			Arrays.fill(prime, true);
			for(int i = 2; i<=n; i++) {
				if(prime[i]) {
					ans.add(i);
				}
				if((long) i*i>n) {
					continue;
				}
				for(int j = i*i; j<=n; j += i) {
					prime[j] = false;
				}
			}
			return ans;
		}

		public static class Debug {
			public static final boolean LOCAL = System.getProperty("ONLINE_JUDGE")==null;

			private static <T> String ts(T t) {
				if(t==null) {
					return "null";
				}
				try {
					return ts((Iterable) t);
				}catch(ClassCastException e) {
					if(t instanceof int[]) {
						String s = Arrays.toString((int[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof long[]) {
						String s = Arrays.toString((long[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof char[]) {
						String s = Arrays.toString((char[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof double[]) {
						String s = Arrays.toString((double[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}else if(t instanceof boolean[]) {
						String s = Arrays.toString((boolean[]) t);
						return "{"+s.substring(1, s.length()-1)+"}";
					}
					try {
						return ts((Object[]) t);
					}catch(ClassCastException e1) {
						return t.toString();
					}
				}
			}

			private static <T> String ts(T[] arr) {
				StringBuilder ret = new StringBuilder();
				ret.append("{");
				boolean first = true;
				for(T t: arr) {
					if(!first) {
						ret.append(", ");
					}
					first = false;
					ret.append(ts(t));
				}
				ret.append("}");
				return ret.toString();
			}

			private static <T> String ts(Iterable<T> iter) {
				StringBuilder ret = new StringBuilder();
				ret.append("{");
				boolean first = true;
				for(T t: iter) {
					if(!first) {
						ret.append(", ");
					}
					first = false;
					ret.append(ts(t));
				}
				ret.append("}");
				return ret.toString();
			}

			public static void dbg(Object... o) {
				if(LOCAL) {
					System.err.print("Line #"+Thread.currentThread().getStackTrace()[2].getLineNumber()+": [");
					for(int i = 0; i<o.length; i++) {
						if(i!=0) {
							System.err.print(", ");
						}
						System.err.print(ts(o[i]));
					}
					System.err.println("]");
				}
			}

		}

	}
}