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:
test_cases = int(input())

def isround(num):
    if int(num) <= 10:
        return 1
    length = len(num)
    if int(num) % pow(10,length-1) ==0:
        return 1
    else:
        return 0

def splitround(num, count, answer):
    if isround(num) ==1:
            answer = answer + num
            count += 1
            print(count)
            print(answer)
            return
    else:
        l = len(num)
        p = pow(10,l-1)
        curr = int(int(num) / p) * p
        answer = answer + str(curr) + " "
        num = int(num) - int(curr)
        num = str(num)
        splitround(num,count+1,answer)

#main execution
for i in range(test_cases):
    n = input()
    if isround(n) == 1:
        print(1)
        print(n)
        continue
    else:
        splitround(n,0,"")