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:
from sys import *
from math import *
from collections import *

mod = 1000000007

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

def read_int(): return int(stdin.readline())

def input(): return stdin.readline()

def main():
	tc = read_int()
	while tc:
		N = read_int()
		arr = []
		power = 1
		while N>0:
			if (N%10 > 0):
				arr.append((N%10) * power)
			N //= 10
			power *= 10
		stdout.write(str(len(arr))+'\n')
		print(*arr)
		tc -= 1

if __name__ == "__main__":
	main()