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:
#include <bits/stdc++.h>
#define SYNC ios_base::sync_with_stdio(0);
#define IO STD std_enable = 1; cin.tie(0);
#define STD /*
from sys import (
stdin, stdout, exit as sys_ret)
"""****************************

       Interactive Tasks:

          / Python: /       """
f_input, f_print, f_flush = (
        stdin.readline,
        stdout.write,
        stdout.flush)

"""        / C++ /
       #import <cstdio>
       fflush(stdout);
             or
       #import <iostream>
       cout << endl;

   —————————————————————————
    Don't raise your voice,
    improve your argument.
   —————————————————————————

   cat /dev/ass > /dev/head
            Ctrl+C
   cat /knowledge > /dev/head

                © Jakov Gellert
                        frvr.ru

****************************"""
# */ using namespace std; int
#define boost_stream(); IO SYNC

for _ in range(int(f_input())):
    number = int(f_input())
    power = 0
    answer = []
    while number:
        last = number % 10
        if last > 0:
            answer.append(last * (10 ** power))
        number //= 10
        power += 1
    f_print(str(len(answer)) + '\n')
    for i in answer:
        f_print(str(i) + ' ')
    f_print('\n')