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:
# -*- coding: utf-8 -*-
"""
Created on Thu May 14 13:00:10 2020

@author: Maarten
"""


def solve(n):
    answer = []
    k = str(n)
    l = len(k)
    for i in range(l-1, -1, -1):
        if k[i] != '0':
            answer.append(int(k[i]) * (10 ** (l-i-1)))
    print(len(answer))
    for i in answer:
        print(i)

if __name__ == '__main__':
    # fptr = open(os.environ['OUTPUT_PATH'], 'w')
    # fptr = open('01.txt')

    # t = int(fptr.readline().strip())
    t = int(input().strip())
    
    # n = []
    for _ in range(t):
        n = int(input().strip())
        # n.append(int(fptr.readline().strip()))
    
        solve(n)
    
    # print('\n'.join(result))          # for strings
    # print(' '.join(map(str, result)))   # for int arrays
    # print('\n'.join(map(str, result)))   # for int arrays
    # print('\n')