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:
numbers = []
true_numbers = []

count = int(input())
for i in range(count):
    n = input()
    numbers.append(n)

for i in numbers:
    if len(i) == 1: # if i is yek raqami
        true_numbers.append(int(i))
    else: #if i > yek raqami
        if int(i)/(int(i[0]) * ( 10**(len(i)-1) ) ) == 1: #check if i is round
            true_numbers.append(i)
        else:        #this is round of first digit,
            '''int(i[0]) * ( 10**(len(i)-1) ),'''
            bad_n = [] 
            #baqi = int(i) % (int(i[0]) * ( 10**(len(i)-1) ) )
            counter = len(i) - 1
            for j in i:
                digit = int(j) * ( 10**counter )
                if digit != 0:
                    bad_n.append(str(digit))
                counter -= 1
            true_numbers.append(bad_n)               


''' printing '''
for q in true_numbers:
    if type(q)==type([]):
        print(len(q))
        print(' '.join(q))
    else:
        print(1)
        print(int(q))