1352A. Sum of Round Numbers

implementation, math, 800, https://codeforces.com/problemset/problem/1352/A

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, 99 800, 90. The following numbers are not round: 110, 707, 222, 1001.

You are given a positive integer $𝑛(1\le 𝑛\le {10}^4)$. Represent the number 𝑛n as a sum of round numbers using the minimum number of summands (addends). In other words, you need to represent the given number 𝑛n as a sum of the least number of terms, each of which is a round number.

Input

The first line contains an integer $𝑡(1\le 𝑡\le {10}^4)$ — the number of test cases in the input. Then 𝑡t test cases follow.

Each test case is a line containing an integer $𝑛(1\le 𝑛\le {10}^4)$.

Output

Print 𝑡t answers to the test cases. Each answer must begin with an integer 𝑘k — the minimum number of summands. Next, 𝑘k terms must follow, each of which is a round number, and their sum is 𝑛n. 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

n = int(input())
for _ in range(n):
    s = input()
    cnt = 0
    res = []
    i = 0
    for c in s:
        i += 1
        if c != '0':
            cnt += 1
            res.append( int(c) * (10 ** (len(s) - i)) )
    print(cnt)
    print(*res)