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())
while t>0:
    t-=1
    n = input()
    li = []
    for x in range(len(n)):
        res = n[x]
        append_all_zeros = False
        for y in range(x+1,len(n)):
            if n[y] > '0':
                append_all_zeros = True
                break
        res  = res + '0'*(len(n) - x-1)
        li.append(res)
        if append_all_zeros == False:
            #because after this no element will be found so now you can come out 
            break   
    final = []
    for x in li:
        for ele in x:
            if ele > '0':
                final.append(x)
                break;
    print(len(final))
    for x in final:
        print(x,end=" ")