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:
def ans(s):
    x = str(s)
    arr = [0]*len(x)
    if len(x) is 1:
        print(1)
        print(int(x))

    else:
        temp = len(x)-1
        for i in range(len(x)):
            arr[i] = (int(x[i])*(10**temp))
            temp-=1
            pass
        count = 0
        for i in range(len(arr)):
            if arr[i] is not 0:
                count+=1
        
        print(count)
        for i in range(len(arr) - 1):
            if arr[i] is not 0:
                print(arr[i], end = ' ')
        
        if arr[len(arr)-1] is 0:
            print()
        else:
            print(arr[len(arr)-1])


    pass


n = int(input())
for i in range(n):
    s = int(input())
    ans(s)