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:
# import nltk
# from math import log
# from matplotlib import pyplot as plt
# import numpy as np
# from nltk.corpus import gutenberg as gb
#
# fdist = nltk.FreqDist(gb.words('burgess-busterbrown.txt'))
# l = fdist.most_common(200)
#
# x = np.arange(1, 201, dtype='float_')
# y = x.copy()
# for i, v in enumerate(x):
#     x[i] = 1.0 * log(1 / v)
# for i, v in enumerate(y):
#     y[i] = log(l[i][1])
#
# plt.plot(x, y)
# plt.show()
T = int(input())
while T:
    T -= 1
    n = input()
    ans = []
    for i, v in enumerate(n):
        if v != '0':
            ans.append(v + '0' * (len(n) - i - 1))
    print(len(ans))
    for i in ans:
        print(i, end=' ')
    print()