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 math import *
from collections import *
from itertools import *
from bisect import *
def io():
    return map(int,input().split())
def op():
    return list(map(int,input().split()))
def kl(con,x=0):
    if x==0:print('Yes') if con else print('No')
    elif x==1:print('yes') if con else print('no')
    elif x==2:print('YES') if con else print('NO')
MOD = 1000000007
MAX=2147483647
MIN=-2147483648
p=input
for _ in range(int(p())):
    l=[]
    s=p()
    n=int(s)
    c=1
    while n:
        x=n%10
        if x!=0:
            l.append(x*c)
        c*=10
        n//=10
    print(len(l))
    print(*l)