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:
list1=[]


n=int(input(""))
for i in range(0,n):
    ele=input()
    list1.append(ele)
# will be broken in how many parts 
for i in list1:
    count=0
    for s in range(0,len(i)):
        
        if i[s]!='0':
            count=count+1
    
    print(count)
    temp=int(i)
    a=temp%10
    if a!=0:
        print(a,end=" ")
    temp=temp//10
    b=temp%10
    if b!=0:
        print(b*10,end=" ")
    temp=temp//10
    c=temp%10
    if c!=0:
        print(c*100)
    temp=temp//10
    d=temp%10
    if d!=0:
        print(d*1000)
    temp=temp//10
    e=temp%10
    if e!=0:
        print(e*10000)