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:
# Coder: cyberdynamo
test=int(input())
def validate(n):
    flag=1
    while(len(str(n))>0):
        d=n%10
        if(d!=0):
            flag=0
            break
        n=n//10
    if(flag==0):
        return False
    else:
        return True
    
for t in range(test):
    lst=[]
    n=int(input())
    if(n>=0 and n<10):
        print(1)
        print(n)
    elif(validate(n)==True):
        print(1)
        print(n)
    else:
        mul=1
        while(n!=0):
            d=n%10
            if(d!=0):
                lst.append(mul*d)
            mul*=10
            n=n//10
        print(len(lst))
        for i in range(len(lst)-1):
            print(lst[i],end=" ")
        print(lst[-1])