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 parse():
    inputs=[]
    nbCase= int(input())
    for i in range(nbCase):
        line=input()
        inputs.append(list(map(int, line.split())))
    return inputs

def write_tab(tab):
    w=""
    for i in range(len(tab)):
        w+=str(tab[i])+" "
    return w

def solve():
    inputs= parse()
    for case in inputs:
        rounds= decomposition(case[0])
        print(len(rounds))
        print(write_tab(rounds))

def decomposition(number):
    rounds=[]
    b=1
    while(number !=0):
        round_b=(number%10)*b
        if round_b !=0: rounds.append(round_b)
        number= number//10
        b*=10
    return list(rounds)

solve()