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:
n=int(input())
for i in range(0,n):
    s=input()
    l=len(s)
    j=0
    count=0
    while j<l:
        if s[j]=="0":
           count=count+1
        j=j+1
    s=int(s)
    print(l-count)
    if l==1:
        print(s)
    else:    
      r=10
      p=[]
      while s!=0:
        k=s%r
        p.append(k)
        s=s//r
        
          
      le=len(p)
      p.reverse()
      
      g=0
      while g<le:
        if p[g]==0:
            pass
        else:
            if g!=le-1:
              print(p[g]*pow(10,le-1-g),end=" ")
            else:
                print(p[g]*pow(10,le-1-g))
        g=g+1