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, os.path

if(os.path.exists('input.txt')):
    sys.stdin = open('input.txt',"r")
    sys.stdout = open('output.txt',"w")

sys.setrecursionlimit(10 ** 5)

def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))

def solve():
    l=list(sys.stdin.readline().strip('\n'))
    print(len(l)-l.count('0'))
    while len(l)!=0:
        if l[0]!='0':
            print(l[0]+'0'*(len(l)-1), end=" ")
            l.remove(l[0])
        else:
            l.remove(l[0])
    print()

for _ in range(II()):
    solve()

# import sys
 
 
# for t in range(int(sys.stdin.readline())):
# 	out = []
 
# 	a = sys.stdin.readline()[:-1]
# 	for c in a:
# 		if c != '0':
# 			out.append("{}{}".format(c, '0'*(len(a)-1)))
 
# 		a = a[1:]
 
 
# 	sys.stdout.write("{}\n".format(len(out)))
# 	sys.stdout.write("{}\n".format(' '.join(out)))


########################################################


# t = int(input())
# def find_solution(x):
#     # x = '9876'
#     round_number = []
#     for idx,i in enumerate(x[::-1]):
#         if i == '0':
#             continue
#         else:
#             round_number.append(i + '0'*idx)
#     print(len(round_number))
#     print(' '.join(round_number))
 
# def main():
#     t = int(input())
#     input_list = [input() for i in range(t)]
#     for i in input_list:
#         find_solution(i)
 
# main()