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:
testcases = int(input())
for test in range(testcases):
    # Input
    n = input()
    # Logic
    k = 0
    k_list = []
    def check_round(num):
        num = str(num)
        # print(f'length:{len(num)}|1st:{num[0]}|rest:{num[1:]}')
        if len(num) != 1:
            # print('Log 1')
            if len(num.rstrip('0')) == 1:
                return True
            else:
                # print('Log 3')
                return False
        # print('Log 4')
        return True
    if check_round(n):
        print(k+1)
        print(n)
    else:
        n = int(n)
        while n != 0:
            j = len(str(n))
            calc_factor = n % 10**(j-1)
            # print(f'n:{n}|calc_factor:{calc_factor}|j:{j}')
            # print(n - calc_factor)
            k_list.append(n - calc_factor)
            k += 1
            n = calc_factor
        print(k)
        for i in k_list:
            print(i,end=' ')
        print()