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:

ndatos = int(input())
numbers = []
for i in range(ndatos):
    numbers.append(input())
    
matrix = []
for i in numbers:
    if len(i) > 1:
        expected = "0"*(len(i)-1)
        
        if i[1::]!=expected:
            rounds = []
            rounds.append(str(i[0]+("0"*(len(i)-1))))
            
            j = 1
            while j<len(i):
                if i[j] != "0":
                    rounds.append(str(i[j]+("0"*(len(i)-j-1))))
                j+=1
            matrix.append(rounds)
        else:
            rounds = []
            rounds.append(i)
            matrix.append(rounds)           
    else:
        rounds = []
        rounds.append(i)
        matrix.append(rounds) 

for j in matrix:
    print(len(j))
    for i in j:
        print(int(i), end= " ")
    print()