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:
def rounded(t):
    n=int(t)  
    f=[]
    while n>9:
        a=n%10
        n=int(n/10)
        f.append(a)
    f.append(n)
    p=len(f)
    for j in range (0,len(f)):
          if f[j]==0:
              p-=1
    print (p)
    u=[]
    for i in range (0,len(f)):
        y=f[i]*(10**i)
        if y!=0:
           u.append(y)
    for i in range (0,len(u)):
          print (u[i],end=" ")

t=int(input())
for i in range (0,t):
    j=input()
    rounded(j)