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:
testcases = int(input())
while(testcases>0):
	testcases = testcases - 1
	number = int(input())
	string = str(number)
	if(string.count('0')==len(string)-1 and string[0]!='0'):
		print(1)
		print(number)
		continue
	else:
		newstring = string[1:] + string[0]
		ans = ""
		for i in range(0,len(string)):
			if(newstring[i]!='0'):
				if(i==len(string)-1):
					ans = ans + " " + newstring[i] + '0'*(len(string)-1)
				else:
					ans = ans + " " + newstring[i] + '0'*(len(string)-i-2)

			'''if(i==0):
				ans = string[0] + '0'*(len(string)-1) + " "
			else:
				ans = string[i] + '0'*(len(string)-1-i) + " " + ans'''
		ans = ans[1:]
		print(ans.count(" ") + 1)
		print(ans)