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:
def SumofRoundNumbers():
    length = int(input())
    numData = [None for _ in range(length)]
    for i in range(length):
        numData[i] = int(input())
    result = []
    for elem in numData:
        num, loc = [0, 0]
        terms = []
        while elem != 0:
            if elem % 10 != 0:
                terms.append(elem % 10 * 10 ** loc)
                num += 1
                
            elem  = elem // 10
            loc += 1
        result.append([num, terms])
    
    for elem in result:
        print(elem[0])
        for term in elem[1]:
            print(term, end="\t")
        if elem != result[-1]:
            print()
            
SumofRoundNumbers()