Problem: A positive (strictly greater than zero) integer is called round if it is of the form d00...0. In other words, a positive integer is round if all its digits except the leftmost (most significant) are equal to zero. In particular, all numbers from 1 to 9 (inclusive) are round.

For example, the following numbers are round: 4000, 1, 9, 800, 90. The following numbers are not round: 110, 707, 222, 1001.

You are given a positive integer n (1 ≤ n ≤ 10^4). Represent the number n as a sum of round numbers using the minimum number of summands (addends). In other words, you need to represent the given number n as a sum of the least number of terms, each of which is a round number.

Input

The first line contains an integer t (1 ≤ t ≤ 10^4) — the number of test cases in the input. Then t test cases follow.

Each test case is a line containing an integer n (1 ≤ n ≤ 10^4).

Output

Print t answers to the test cases. Each answer must begin with an integer k — the minimum number of summands. Next, k terms must follow, each of which is a round number, and their sum is n. The terms can be printed in any order. If there are several answers, print any of them.

Example

Input


5
5009
7
9876
10000
10


Output


2
5000 9
1
7 
4
800 70 6 9000 
1
10000 
1
10 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    int N;

    void solve(int n) {
        if (n < 10) {
            System.out.println(1);
            System.out.println(n);
        } else {
            List<Integer> list = new ArrayList<>();
            int times = 1;
            while (n > 0) {
                int mod = n % 10;
                if (mod > 0)  list.add(mod * times);
                times *= 10;
                n = (int) Math.floor( n / 10);
            }
            StringBuilder sb = new StringBuilder();
            System.out.println(list.size());
            for (int i = 0; i < list.size(); i++) {
                int a = list.get(i);
                if (i == list.size() - 1) System.out.print(a);
                else System.out.print(a + " ");
            }
            System.out.println("");
        }
    }

    void main(FastScanner in, PrintWriter out) {
        N = in.nextInt();
        for (int i = 0; i < N; i++) {
            solve(in.nextInt());
        }
    }

    public static void main(String[] args) throws Exception {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Main m = new Main();
        m.main(in, out);
        out.close();
        in.close();
    }

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        public FastScanner(InputStream in) { br = new BufferedReader(new InputStreamReader(in)); }
        public int nextInt() { return Integer.parseInt(next()); }
        public long nextLong() { return Long.parseLong(next()); }
        public double nextDouble() { return Double.parseDouble(next()); }
        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try { st = new StringTokenizer(br.readLine()); }
                catch (IOException e) { e.printStackTrace(); }
            }
            return st.nextToken();
        }
        public String nextLine() {
            String str = "";
            try { str = br.readLine();
            } catch (IOException e) { e.printStackTrace(); }
            return str;
        }
        public void close() throws IOException { br.close(); }
    }
}