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.*;

@SuppressWarnings("unused")
public class Main {
  static class FactorL {

    static long[][] factorX(long n, int[] primes) {
      long[][] ret = new long[20][2];
      int rp = 0;
      for (int p : primes) {
        if ((long) p * p > n)
          break;
        int i;
        for (i = 0; n % p == 0; n /= p, i++)
          ;
        if (i > 0) {
          ret[rp][0] = p;
          ret[rp][1] = i;
          rp++;
        }
      }
      if (n == 1)
        return Arrays.copyOf(ret, rp);

      // P^2
      long sq = (long) Math.sqrt(n);
      for (long u = Math.max(2, sq - 2); u <= sq + 2; u++) {
        if (u * u == n) {
          ret[rp][0] = u;
          ret[rp][1] = 2;
          rp++;
          return Arrays.copyOf(ret, rp);
        }
      }

      // Prime
      if (doMirrorRabin(n)) {
        ret[rp][0] = n;
        ret[rp][1] = 1;
        rp++;
        return Arrays.copyOf(ret, rp);
      }

      // P*Q
      long f = rho(n);
      if (f == -1)
        throw new ArithmeticException();
      if (f > n / f)
        f = n / f;
      ret[rp][0] = f;
      ret[rp][1] = 1;
      rp++;
      ret[rp][0] = n / f;
      ret[rp][1] = 1;
      rp++;
      return Arrays.copyOf(ret, rp);
    }

    public static long mul(long a, long b, long mod) {
      a %= mod;
      long ret = 0;
      int x = 63 - Long.numberOfLeadingZeros(b);
      for (; x >= 0; x--) {
        ret += ret;
        if (ret >= mod)
          ret -= mod;
        if (b << ~x < 0) {
          ret += a;
          if (ret >= mod)
            ret -= mod;
        }
      }
      return ret;
    }

    public static boolean doMirrorRabin(long n) {
      // int[] P = {2, 7, 61}; // n<4759123141
      int[] P = { 2, 3, 5, 7, 11, 13, 17, 19, 23 }; // n=long
      int s = Long.numberOfTrailingZeros(n - 1);
      long d = n - 1 >> s;
      outer: for (int a : P) {
        if (a >= n)
          continue;

        long mul = a;
        long ad = 1;
        for (long e = d; e > 0; e >>>= 1) {
          if ((e & 1) == 1)
            ad = mul(ad, mul, n);
          mul = mul(mul, mul, n);
        }
        if (ad == 1)
          continue;

        for (int r = 0; r < s; r++) {
          if (ad == n - 1)
            continue outer;
          ad = mul(ad, ad, n);
        }
        return false;
      }
      return true;
    }

    static long rho(long n) {
      Random gen = new Random();
      for (int u = 0; u < 100; u++) {
        long ran = (gen.nextLong() & Long.MAX_VALUE) % n;
        long x = 2, y = 2, d = 1;
        while (d == 1) {
          x = (mul(x, x, n) + ran) % n;
          y = (mul(y, y, n) + ran) % n;
          y = (mul(y, y, n) + ran) % n;
          d = gcd(Math.abs(x - y), n);
        }
        if (d < n)
          return d;
      }
      return -1;
    }

    public static long gcd(long a, long b) {
      while (b > 0) {
        long c = a;
        a = b;
        b = c % b;
      }
      return a;
    }

    public static int[] sieveEratosthenes(int n) {
      if (n <= 32) {
        int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
        for (int i = 0; i < primes.length; i++) {
          if (n < primes[i]) {
            return Arrays.copyOf(primes, i);
          }
        }
        return primes;
      }

      int u = n + 32;
      double lu = Math.log(u);
      int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
      ret[0] = 2;
      int pos = 1;

      int[] isp = new int[(n + 1) / 32 / 2 + 1];
      int sup = (n + 1) / 32 / 2 + 1;

      int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
      for (int tp : tprimes) {
        ret[pos++] = tp;
        int[] ptn = new int[tp];
        for (int i = (tp - 3) / 2; i < tp << 5; i += tp)
          ptn[i >> 5] |= 1 << (i & 31);
        for (int i = 0; i < tp; i++) {
          for (int j = i; j < sup; j += tp)
            isp[j] |= ptn[i];
        }
      }

      // 3,5,7
      // 2x+3=n
      int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4, 13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17,
          9, 6, 16, 5, 15, 14 };
      int h = n / 2;
      for (int i = 0; i < sup; i++) {
        for (int j = ~isp[i]; j != 0; j &= j - 1) {
          int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
          int p = 2 * pp + 3;
          if (p > n)
            break;
          ret[pos++] = p;
          for (int q = pp; q <= h; q += p)
            isp[q >> 5] |= 1 << (q & 31);
        }
      }

      return Arrays.copyOf(ret, pos);
    }
  }

  private static void solve() {
    int t = ni();
    for (int i = 0; i < t; i++) {
      long n = nl();
      long[] a = solve(n);
      StringBuilder sb = new StringBuilder();
      for (long v : a) {
        sb.append(v + " ");
      }
      out.println(a.length);
      out.println(sb.substring(0, sb.length() - 1));
    }
  }

  static int[] primes = FactorL.sieveEratosthenes(1000000);

  private static long[] solve(long n) {
    long[][] f = FactorL.factorX(n, primes);

    Arrays.sort(f, (o1, o2) -> Long.signum(o2[1] - o1[1]));
    int k = (int) f[0][1];
    long[] ret = new long[k];
    ret[k - 1] = n;

    for (int i = 0; i < k - 1; i++) {
      ret[k - 1] /= f[0][0];
      ret[i] = f[0][0];
    }
    return ret;
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

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

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}