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 PYTHON):

Solution:
test_cases=int(raw_input())
while test_cases >0:
    input=int(raw_input())
    input=str(input)
    length=len(input)
    input=int(input)
    if input<10:
        print str(1) + '\n' +str(input)
    elif input%10**(length-1)==0:
        print str(1)
        print input
    else:
        terms=[]
        L=length
        while L!=0:
            term=input/10**(L-1) * 10**(L-1)
            terms.append(term)
            input-=term
            L-=1
        n=terms.index(term)
        while n+1>0:
            for term in terms:
                if term==0:
                    terms.remove(term)
            n-=1
                
        print (terms.index(term)+1)
        print (' '.join(map(str, terms)))
    test_cases -=1