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:
t = int(input())
while t > 0:
	t -= 1
	n = str(input())
	dum = []
	for i in n:
	    i = int(i)
	    dum += [i]	    
	x = len(dum)
	x1 = len(dum)
	ans = []
	y = 0
	while x > 0:
	    z = dum[y]
	    if z != 0:
	        ans += [y]
	    x -= 1
	    y += 1
	ansL = []
	while len(ans) > 0:
	    z = ans[0]
	    te = x1 - (z + 1)
	    d1 = dum[z]
	    d2 = d1 * (10 ** te)
	    ansL += [d2]
	    ans.pop(0)
	a = len(ansL)
	print(a)
	while a > 0:
	    print(ansL[0],end = " ")
	    ansL.pop(0)
	    a -= 1
	print()