Problem: You are given an integer n (n > 1).

Your task is to find a sequence of integers a_1, a_2, …, a_k such that:

  * each a_i is strictly greater than 1; 
  * a_1 ⋅ a_2 ⋅ … ⋅ a_k = n (i. e. the product of this sequence is n); 
  * a_{i + 1} is divisible by a_i for each i from 1 to k-1; 
  * k is the maximum possible (i. e. the length of this sequence is the maximum possible). 



If there are several such sequences, any of them is acceptable. It can be proven that at least one valid sequence always exists for any integer n > 1.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 5000) — the number of test cases. Then t test cases follow.

The only line of the test case contains one integer n (2 ≤ n ≤ 10^{10}).

It is guaranteed that the sum of n does not exceed 10^{10} (∑ n ≤ 10^{10}).

Output

For each test case, print the answer: in the first line, print one positive integer k — the maximum possible length of a. In the second line, print k integers a_1, a_2, …, a_k — the sequence of length k satisfying the conditions from the problem statement.

If there are several answers, you can print any. It can be proven that at least one valid sequence always exists for any integer n > 1.

Example

Input


4
2
360
4999999937
4998207083


Output


1
2 
3
2 2 90 
1
4999999937 
1
4998207083 

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.Random;
import java.io.FileWriter;
import java.io.PrintWriter;
/*
    Solution Created: 06:28:59 25/11/2020
    Custom Competitive programming helper.
*/

public class Main {
	public static void solve(Reader in, Writer out) {
		int t = in.nextInt();
		while(t-->0){
			long n = in.nextLong();
			ArrayList<Long> ans = maxBreak(n,1);
			out.println(ans.size());
			for(Long i : ans) out.print(i+" ");
			out.println();
		}
	}
	public static ArrayList<Long> maxBreak(long v, long prev){
		ArrayList<Long> ans = new ArrayList<>();
		ans.add(v);
		for(long i = 2; i*i<=v; i++){
			if(v%i!=0 || (v/i)%i!=0 || i%prev!=0) continue;
			ArrayList<Long> get = maxBreak(v/i,i);
			if(get.size()+1>ans.size()){
				get.add(0, i);
				ans = get;
			}
		}
		return ans;
	}
	public static void main(String[] args) {
		Reader in = new Reader();
		Writer out = new Writer();
		solve(in, out);
		out.exit();
	}

static class Reader {
	static BufferedReader br;
	static StringTokenizer st;
	private int charIdx = 0;
	private String s;

	public Reader() {
		this.br = new BufferedReader(new InputStreamReader(System.in));
	}
	
	public Reader(String f){
		try {
			this.br = new BufferedReader(new FileReader(f));
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	public int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}

	public double[] nd(int n) {
		double[] a = new double[n];
		for (int i = 0; i < n; i++)
			a[i] = nextDouble();
		return a;
	}

	public char nextChar() {
		if (s == null || charIdx >= s.length()) {
			if (st == null || !st.hasMoreTokens())
				try {
					readLine();
				} catch (Exception e) {
				}
			s = st.nextToken();
			charIdx = 0;
		}
		return s.charAt(charIdx++);
	}

	public long[] nl(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++)
			a[i] = nextLong();
		return a;
	}

	public char[] nca() {
		return next().toCharArray();
	}

	public String[] nS(int n) {
		String[] a = new String[n];
		for (int i = 0; i < n; i++)
			a[i] = next();
		return a;
	}

	public int nextInt() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return Integer.parseInt(st.nextToken());
	}

	public double nextDouble() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return Double.parseDouble(st.nextToken());
	}

	public Long nextLong() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return Long.parseLong(st.nextToken());
	}

	public String next() {
		if (st == null || !st.hasMoreTokens())
			try {
				readLine();
			} catch (Exception e) {
			}
		return st.nextToken();
	}

	public static void readLine() {
		try {
			st = new StringTokenizer(br.readLine());
		} catch (Exception e) {
		}
	}
}

static class Util{
		private static Random random = new Random();
		static long[] fact;
		public static void initFactorial(int n, long mod) {
			fact = new long[n+1];
			fact[0] = 1;
			for (int i = 1; i < n+1; i++) fact[i] = (fact[i - 1] * i) % mod;
		}
		public static long modInverse(long a, long MOD) {
			long[] gcdE = gcdExtended(a, MOD);
			if (gcdE[0] != 1) return -1; // Inverted doesn't exist
			long x = gcdE[1];
			return (x % MOD + MOD) % MOD;
		}
		public static long[] gcdExtended(long p, long q) {
			if (q == 0) return new long[] { p, 1, 0 };
			long[] vals = gcdExtended(q, p % q);
			long tmp = vals[2];
			vals[2] = vals[1] - (p / q) * vals[2];
			vals[1] = tmp;
			return vals;
		}
		public static long nCr(int n, int r, long MOD) {
			if (r == 0) return 1;
			return (fact[n] * modInverse(fact[r], MOD) % MOD * modInverse(fact[n - r], MOD) % MOD) % MOD;
		}
		public static long nCr(int n, int r) {
			return (fact[n]/fact[r])/fact[n-r];
		}
		public static long nPr(int n, int r, long MOD) {
			if (r == 0) return 1;
			return (fact[n] * modInverse(fact[n - r], MOD) % MOD) % MOD;
		}
		public static long nPr(int n, int r) {
			return fact[n]/fact[n-r];
		}
		public static boolean isPrime(int n) { 
	        if (n <= 1) return false; 
	        if (n <= 3) return true; 
	        if (n % 2 == 0 || n % 3 == 0) return false; 
	        for (int i = 5; i * i <= n; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	        return true; 
	    }
		public static boolean isPrime(long n) { 
	        if (n <= 1) return false; 
	        if (n <= 3) return true; 
	        if (n % 2 == 0 || n % 3 == 0) return false; 
	        for (long i = 5; i * i <= n; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	            return false; 
	        return true; 
	    }
	    public static int lowerBound(int[] a, int v) {
	    	int l = 0, h = a.length;
	    	while(l<h) {
	    		int mid = (l+h)/2;
	    		if(v<=a[mid]) h = mid;
	    		else l = mid+1;
	    	}
	    	return l;
	    }
	    public static int lowerBound(long[] a, long v) {
	    	int l = 0, h = a.length;
	    	while(l<h) {
	    		int mid = (l+h)/2;
	    		if(v<=a[mid]) h = mid;
	    		else l = mid+1;
	    	}
	    	return l;
	    }
	    public static int upperBound(int[] a, int v) {
	    	int l = 0, h = a.length;
	    	while(l<h) {
	    		int mid = (l+h)/2;
	    		if(a[mid]<=v) l = mid+1;
	    		else h = mid;
	    	}
	    	return l;
	    }
	    public static int upperBound(long[] a, long v) {
	    	int l = 0, h = a.length;
	    	while(l<h) {
	    		int mid = (l+h)/2;
	    		if(a[mid]<=v) l = mid+1;
	    		else h = mid;
	    	}
	    	return l;
	    }
	    public static boolean[] getSieve(int n) {
	        boolean[] isPrime = new boolean[n+1];
	        for (int i = 2; i <= n; i++) isPrime[i] = true;
	        for (int i = 2; i*i <= n; i++) if (isPrime[i]) 
	                for (int j = i; i*j <= n; j++) isPrime[i*j] = false;
	        return isPrime;
	    }
	    public static int gcd(int a, int b) { 
	    	int tmp = 0;
	    	while(b != 0) {
	    		tmp = b;
	    		b = a%b;
	    		a = tmp;
	    	}
	    	return a;
	    }
	    public static long gcd(long a, long b) { 
	    	long tmp = 0;
	    	while(b != 0) {
	    		tmp = b;
	    		b = a%b;
	    		a = tmp;
	    	}
	    	return a;
	    }
	    public static int random(int min, int max) {
	    	return random.nextInt(max-min+1)+min;
	    }
		public static void dbg(Object... o) { 
			System.out.println(Arrays.deepToString(o)); 
		}
		public static void reverse(int[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				int tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		public static void reverse(int[] s) {
			reverse(s, 0, s.length-1);
	    }
		public static void reverse(long[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				long tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		public static void reverse(long[] s) {
			reverse(s, 0, s.length-1);
	    }
		public static void reverse(float[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				float tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		public static void reverse(float[] s) {
			reverse(s, 0, s.length-1);
	    }
		public static void reverse(double[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				double tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		public static void reverse(double[] s) {
			reverse(s, 0, s.length-1);
	    }
		public static void reverse(char[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				char tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		public static void reverse(char[] s) {
			reverse(s, 0, s.length-1);
	    }
		public static <T> void reverse(T[] s, int l , int r) {
			for(int i = l; i<=(l+r)/2; i++) {
				T tmp = s[i];
				s[i] = s[r+l-i];
				s[r+l-i] = tmp;
			}
	    }
		public static <T> void reverse(T[] s) {
			reverse(s, 0, s.length-1);
	    }
		public static void shuffle(int[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            int t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    public static void shuffle(long[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            long t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    public static void shuffle(float[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            float t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    public static void shuffle(double[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            double t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    public static void shuffle(char[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            char t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
	    public static <T> void shuffle(T[] s) {
	        for (int i = 0; i < s.length; ++i) {
	            int j = random.nextInt(i + 1);
	            T t = s[i];
	            s[i] = s[j];
	            s[j] = t;
	        }
	    }
		public static void sortArray(int[] a) {
	        shuffle(a);
	        Arrays.sort(a);
	    }
		public static void sortArray(long[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		public static void sortArray(float[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		public static void sortArray(double[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		public static void sortArray(char[] a) {
			shuffle(a);
	        Arrays.sort(a);
	    }
		public static <T extends Comparable<T>> void sortArray(T[] a) {
	        Arrays.sort(a);
	    }
	}

static class Writer {
	private PrintWriter pw;
	public Writer(){
		pw = new PrintWriter(System.out);
	}
	
	public Writer(String f){
		try {
			pw = new PrintWriter(new FileWriter(f));
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	public void printArray(int[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
	}
	public void printlnArray(int[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
		pw.println();
	}
	public void printArray(long[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
	}
	public void printlnArray(long[] a) {
		for(int i = 0; i<a.length; i++) print(a[i]+" ");
		pw.println();
	}
	public void print(Object o) {
		pw.print(o.toString());
	}
	public void println(Object o) {
		pw.println(o.toString());
	}
	public void println() {
		pw.println();
	}
	public void flush() {
		pw.flush();
	}
	public void exit() {
		pw.close();
	}
}
}