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:
# Importing Modules
from collections import *
from itertools import *
from functools import *
import sys
import os
import time
# ~ import numpy as np


# Debugging and Timer Flags
timer = False
debug = False

# ---------- Helper Functions -----------
def timeit(method):
    def wrapper(*args, **kwargs):
        mname = method.__name__
        if debug:
            print("{}(args:{}, kwargs:{})".format(mname, args,kwargs))
        if timer:
            ts = time.time()
        result = method(*args, **kwargs)
        if timer:
            te = time.time()
            print('%r  %2.2f ms'% (mname, (te-ts) * 1000))
        return result
    return wrapper

def read_ints():
    return list(map(int,input().split()))

def read_floats():
    return list(map(float,input().split()))

def read_strs():
    return input().split()
# ----------------------------------------




@timeit
def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        ans = []
        i = 0
        while n:
            if n%10!=0:
                ans.append((n%10)*(10**i))
            i+=1
            n//=10
        print(len(ans))
        print(*ans[::-1])

if __name__=="__main__":
    main()