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:
from sys import stdin

input = stdin.readline


def main():
    test = int(input())

    for t in range(test):
        n = int(input())
        # l = [int(i) for i in input().split(" ")]
        # n = l[0]
        # k = l[1]
        # l = [int(i) for i in input().split(" ")]
        count = 0
        l = []
        c = 0

        while n > 0:
            if n % 10 != 0:
                l.append((n % 10)*pow(10,c))
                count += 1
            n = n//10
            c += 1

        print(count)
        for i in l:
            print(i, end=' ')
        print()


main()