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:
t = int(input())
s = ''
for i in range(t):
    s1 = ''
    s2 = ''
    s3 = ''
    s4 = ''
    s5 = ''
    s = ''
    k = 0
    a = int(input())
    s5 = str(a % 10)
    s4 = str(a // 10 % 10 * 10)
    s3 = str(a // 100 % 10 * 100)
    s2 = str(a // 1000 % 10 * 1000)
    s1 = str(a // 10000 * 10000)
    if s1 != '0':
        s = s + s1 + ' '
        k += 1
    if s2 != '0':
        s = s + s2 + ' '
        k += 1
    if s3 != '0':
        s = s + s3 + ' '
        k += 1
    if s4 != '0':
        s = s + s4 + ' '
        k += 1
    if s5 != '0':
        s = s + s5 + ' '
        k += 1
    print(k)
    print(s)