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:
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 
#      .      '                    Udit Gupta @luctivud         ,              
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                            ##     ##  #######  # #  ######
                            ##     ##  ##   ##  ###    ##
                            ##     ##  ##    #  # #    ##
                            #########  #######  # #    ##
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

import sys
import math as mt
# sys.setrecursionlimit(10**6)

def get_ints(): return map(int, sys.stdin.readline().strip().split())
def get_array(): return list(map(int, sys.stdin.readline().strip().split()))

def printwsp(*args): return print(*args, end="")
def printsp(*args): return print(*args, end=" ")
def printchk(*args): return print(*args, end="tst, ")

MOD = int(1e9+7); BABYMOD = 998244353;
# ################################ HELPER PROGRAMS USED ###################################
# ################################## MAIN STARTS HERE #####################################
for _testcases_ in range(int(input())):
	n = int(input())
	i = 0
	li = list()
	while(n):
		ab = (n % 10) * pow(10, i)
		if ab:
			li.append(ab)
		i += 1
		n //= 10
	print(len(li))
	for i in li:
		printsp(i)
	print()




# #########################################################################################
'''
THE LOGIC AND APPROACH WAS DEVELOPED BY ME @luctivud.
SOME PARTS OF THE CODE HAS BEEN TAKEN FROM WEBSITES LIKE::
(I Own the code if no link is provided here or I may have missed mentioning it)
PLEASE DO NOT PLAGIARISE.
'''