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:
t=int(input())
for i in range(1,t+1):
    l=[]
    
    n=int(input())
    c=n
    d=0
    while(c>0):
        d+=1
        c=c//10
    
    if(n%(10**(d-1))==0):
        print("1")
        print(n)
    else:
        for j in range(1,d):
            e=n%10**j
            if(e!=0):
                l.append(e)
            
                   
            n-=e
        l.sort(reverse=True)
        l.append(n)
        print(len(l))
        for j in range(len(l)):
            print(l[j],end=" ")
        print("\n")