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())
a = []
b = []
for i in range(n):
    a1 = int(input())
    a.append(int(a1))
for i in range(n):
    if a[i]%(10**(len(str(a[i]))-1))==0 or len(str(a[i]))==1:
        print(1)
        print(a[i])
    else:
        a1 = 0
        s = 0  
        b.clear()
        for j in range(len(str(a[i]))):  
            if len(str(a[i]))!= j: 
                a1 = a[i]%10**(j+1)
                a1 = (a1//(10**j))*(10**j)
                if a1 != 0:   
                    b.append(a1)
                    s+=1
            if len(str(a[i]))==j:
                a1 = a[i]//(10**(len(str(a[i]))-1))  
                b.append(a1)
        print(s)
        print(*b)