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:
n, t, sp= int(input()), 0, []
for i in range(n):
    sp = []
    t = int(input())
    k = 1
    while True:                             # ���� ������� ����� ������� ���� � ������ �������
        sp.append(t % 10)                   # ��������:
        t = t // 10                         # 5009  ����������� � ������ [ 9,0,0,5]
        if t == 0:
            break
    for i in range(len(sp)):               # ���� ���������� ������ � ���������� �������
        sp[i] *= 10**i                     # [9,0,0,5]  -> [9,0,0,5000]
    while True:                            # ���� ������� ������ ������� [9,0,0,5000] -> [9,5000] 
        if 0 in sp:
            sp.pop(sp.index(min(sp)))
        if not(0 in sp):
            break
    print(len(sp))                         #�����
    print(*sp)