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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-
"""
Created on Sat May  9 19:19:01 2020

@author: vushesh
"""

T = int(input())

for _ in range(T):
    
    value = input()
    
    if int(value) <= 9:
        print(1)
        print(value)
        continue
    
    ans = []

    temp = value[0]
    for i in range(1,len(value)):
        temp += '0'
        
    ans.append(int(temp))
    
    for i in range(1,len(value)):
        
        
        if value[i] == '0' :
            continue
        
        else:
            temp = value[i]
            for j in range(i+1,len(value)):
                temp += '0'
                
            ans.append(int(temp))
        
        
    print(len(ans))
    for i in ans:
        print(i,end = ' ')
        
    print()