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:
from sys import stdin
from sys import stdout


sprint = stdout.write
sinput = stdin.readline

#[int(x) for x in sinput().split()]
#int(sinput())


def func():
    num = sinput()
    ans = []
    a = 0
    for i in range(len(num)-1):
       # print(num[i]+'0'*(len(num)-2-i),end=' ') if num[i] != '0' else print('',end='')
        if num[i] != '0':
            ans.append(num[i]+'0'*(len(num)-2-i))
            a += 1
    print(a)
    ans = str(ans).replace('[','').replace(']','').replace("'",'').replace(',','')
    print(ans)


if __name__ == "__main__":
    t = int(sinput())
    while t != 0:
        if t == 1000-84+1+t:
            int(sinput())
            sprint()
            t -= 1
        else:
            t -= 1
            func()