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.util.*;
import java.io.*;

public class a
{
    static boolean multiple_testcases = true;
        
    static void solve() {
        int n = in.nextInt();
        int cnt=1;
        ArrayList<Integer> sol = new ArrayList<>();
        while(n >0) {
            int bit = n%10;
            n /=10;
            if(bit!=0) sol.add(bit*cnt);
            cnt *= 10; 
        }

        System.out.println(sol.size());    
        for(int ele: sol) System.out.print(ele+" ");    
    }
    
    static FastReader in = new FastReader();
    static int INF = Integer.MAX_VALUE;
    public static void main(String[] args) { 
        if(multiple_testcases) {
            int t = in.nextInt();
            while(t-- >0)  solve();
        } else solve();
    }

    static class FastReader { 
        BufferedReader br; StringTokenizer st; 
        public FastReader() { 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()); } 
        char nextChar() { return next().charAt(0); }
        String nextLine() { String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } 
        return str; }
     
        int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for(int i=0;i<n;i++) 
                arr[i] = in.nextInt();
            return arr;    
        } 
    } 
}