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())
for _ in range(t):
    n=int(input())
    z=str(n)
    l=len(z)
    num=10**(l-1)
    if n>9:
        if n/num==1.0 or n/num==2.0 or n/num==3.0 or n/num==4.0 or n/num==5.0 or n/num==6.0 or n/num==7.0 or n/num==8.0 or n/num==9.0:
            print(1)
            print(n)
        else:
            lis=list(z)
            c=0
            my=[]
            for i in range(len(lis)):
                if lis[i]!='0':
                    c+=1
                    s=lis[i]+'0'*(len(lis)-i-1)
                    my.append(s)
            print(c)
            for ch in my:
                print(ch,end=" ")
            print()
    else:
        print(1)
        print(n)