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:
"https://codeforces.com/contest/1328/problem/A"
import collections, heapq, itertools, math
groupby = itertools.groupby
rs  = lambda: input()
ri  = lambda: int(input())
rm  = lambda: map(int, input().split())
rai = lambda: [int(x) for x in input().split()]


def solve(n):
    zero = 0
    ans = []
    N = len(str(n))
    for i,num in enumerate(str(n)):
        if num != '0':
            ans.append(num + '0'*(N-i-1))
    
    return len(ans), ans

for t in range(ri()):
    n = ri()
    a, b = solve(n)
    print(a)
    print(*b)