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:
num_of_test = int(input())
 
for item in range(num_of_test):
    # print(int(input())+int(input()))
    # a,b = s.split(" ")
    # print(int(a)+int(b))
    
    num = int(input())
    op = []
    # num = 465
    if num < 10:
        op.append(str(num))
    else:
        n = len(str(num))
        numlist = list(str(num))
        start = 1
        for item in range(n-1):
            num_m = int("".join(numlist[start:]))
            t_op = num - num_m
            if t_op == 0:
                pass
            elif t_op == num:
                op.append(str(num))
                break
            elif num_m < 10:
                op.append(str(t_op))
                op.append(str(num_m))
                break
            else:
                op.append(str(t_op))
                num = num_m
            start += 1
 
    print(str(len(op)))
    print(" ".join(op))