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:
import pdb

test_cases = int(input())

for tests in range(test_cases):
    #pdb.set_trace()
    counter = 0
    result = []
    temp = 1
    first_number = 0
    n = input()
    for xyz in range(0,len(n)):
        if n[xyz] != "0":
            counter += 1
    print(counter)
        
    for digit in range(len(n)-1, -1, -1):
        if n[digit] != "0" and digit != 0:
            c = int(n[digit]) * temp
            #result.append(c)
            print(c, end=" ")
        temp *= 10

    if digit == 0:
        first_number = int(int(n[0]) * temp / 10)
        print(first_number)
        

    #print(result)