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:
k=int(input())
new=''
l=[]
b=[]
if k>=1 and k<=10000:
    for i in range(0,k):
        n=int(input())
        p=len(str(n))-1
        
        if n>=1 and n<=10000:
            count=1
            while(n>10 and p!=0):
                t=(10**p)
                d=n//t
            
                n=n%t
                p=p-1
                if (d*t)!=0:
                    count=count+1
                    new+=str(d*t)+'  '
            if n==0:
                count-=1
                b.append(count)
                l.append(new)
            else:
                new+=str(n)
                b.append(count)
                l.append(new)

            new=''

for h in range(0,k):
    print(b[h])
    print(l[h])