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.math.*;
import java.util.*;


public class Main{
    static long MOD = 998244353 ;
    static long [] fac;
    static int [] num;

    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        // Start writing your solution here. -------------------------------------
        int t = sc.nextInt();
        //int t = 1;
        while(t-- > 0)
        {
            int n = sc.nextInt();
            int len = (n + "").length();
            List<Integer> list = new ArrayList<>();
            String num = n + "";
            for(int i = 0; i < len; i++)
            {
                char tmp = num.charAt(i);
                if(tmp != '0')
                    list.add((tmp - '0') * (int)Math.pow(10, len - i - 1));
            }
            out.println(list.size());
            for(int i : list)
                out.print(i + " ");
            out.println("");
            //int m = sc.nextInt();
            /*
            int m = sc.nextLong();
            int[] a = new int[n];
            for(int i = 0; i < n; i++)
                a[i] = sc.nextInt();

             */

        //else out.println("NO");
        }
        out.close();
    }
    /*
    public static void dfs(int ind, int now)
    {
        if(ind > n)
        {
            cnt++;
            int sum = 0;
            for(int i = 0; i < q; i++)
            {
                if(num[b[i]] - num[a[i]] == c[i])
                sum += d[i];
            }
            if(sum > max)
                max = sum;
            return;
        }
        for(int j = now; j <= m; j++)
        {
            num[ind] = j;
            dfs(ind + 1, j);
        }
    }*/
    public static long C(int n, int m)
    {
        if(m == 0 || m == n) return 1l;
        if(m > n || m < 0) return 0l;
        long res = fac[n] * quickPOW((fac[m] * fac[n - m]) % MOD, MOD - 2) % MOD;

        return res;
    }
    public static long quickPOW(long n, long m)
    {
        long ans = 1l;
        while(m > 0)
        {
            if(m % 2 == 1)
                ans = (ans * n) % MOD;
            n = (n * n) % MOD;
            m >>= 1;
        }
        return ans;
    }
    public static int gcd(int a, int b)
    {
        if(a % b == 0) return b;
        return gcd(b, a % b);
    }
    public static long solve(long x, long[] res){
        int n = res.length;
        long a = x / n;
        int b = (int)(x % n);
        return res[n - 1] * a + res[b];
    }
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}