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:
import sys
import random
import math
from sys import stdin, stdout 
def get_ints(): return list(map(int, sys.stdin.readline().strip().split()))
def get_string(): return sys.stdin.readline().strip() 
n =int(input())
a=[0]*int(n)
for i in range(0,n):
	a[i] = int(input())
	
for i in range(0,n):
	k=0
	s=[0]*5
	d=0
	while a[i] >0 :
		if a[i] %10 == 0 :
			a[i]//=10
			d+=1
		else :
			s[k]=a[i]%10*(10**d)
			a[i]//=10	
			k+=1
			d+=1
	print(k)
	print(*s[:k])
	
	
	#for k in range(a[i]) :
	#	stdout.write(str(str(s)+' '))
	#print()