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())

while t:
    n = input()
    #num=int(n)
    it = len(n)
    list = []
    count = 0
    i = 0

    while i<it:


                if (it-1-i)==0:

                         temp = int(n[i])

                         if temp!=0:
                              count = count + 1
                              list.append(temp)

                else:
                    k=1
                    z=10
                    while k<(it-1-i):
                                    z=z*10
                                    k=k+1



                    temp = int(n[i])
                    temp = temp * z
                    if temp != 0:
                        count = count + 1
                        list.append(temp)


                i = i + 1

    print(count)
    for item in list:
        if item!=0:
            print(item,end=" ")
    print("")
    t=t-1