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 PYTHON):

Solution:
import sys

__author__ = 'ratmir'

from collections import deque

alphabet = "abcdefghijklmnopqrstuvwxyz"

def solve(n, a, graph):
    return 1

def execute():
    [t] = [int(x) for x in sys.stdin.readline().split()]
    results = []
    for ti in range(0, t):
        [n] = [int(x1) for x1 in sys.stdin.readline().split()]
        v = str(n)
        j = 0
        res = ""
        for i in range(0, len(v)):
            if v[i]!="0":
                res += " "+v[i]
                res += "0"*(len(v)-i-1)
                j += 1


        results.append(str(j)+"\n"+res[1:]+"\n")
    print(''.join('{}'.format(k) for k in results))


execute()