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 = int(input())

j = [1, 2, 3, 4, 5, 6, 7, 8, 9]

for y in range(n):
    z= input()
    l=[int(i) for i in str(z)]
    # print(l)
    ans =[]
    start=0
    # print(len(l))
    for i in range(len(l)-1,-1,-1):

        if l[i] in j and i==len(l)-1:
            ans.append(l[i])

        if l[i]!=0 and i!=len(l)-1:
            # print(i)
            ans.append(l[i]*(10**(len(l)-i-1)))
            # print(ans)
    print(len(ans))
    strings = [str(i) for i in ans]
    print(" ".join(strings))
    ans.clear()