human
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 
The above is tricky. Write me a correct solution in PYTHON.
 ... What is a Python code to print t answers to the test cases?
assistant
#Here is Python code to print t answers to the test cases.

#import collections
FAST_IO = 0
if FAST_IO:
    import io, sys, atexit
    rr = iter(sys.stdin.read().splitlines()).next
    sys.stdout = _OUTPUT_BUFFER = io.BytesIO()
    @atexit.register
    def write():
        sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
else:
    rr = raw_input
rri = lambda: int(rr())
rrm = lambda: map(int, rr().split())
#MOD = 998,244,353 
a = []
for i in range(8180):
	a.append(i*(3*i+1)//2)
def solve(n):
	r = []
	i = 0
	while(n):
		if n%10 != 0:
			r.append((n%10)*(10**i))
		n = n//10
		i += 1
	x = len(r)
	print x
	for i in range(x):
		print r[i],
	print ""

T = rri()
for t in xrange(1, T+1):
	n = rri()
	#a = rr()
	solve(n)