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())
r =[]
e =[]
g =[]
A =[]
for i in range(t):
    r =[]
    g =[]
    s = " "
    n = int(input())
    o = n
    cnt = 1
    d = 10
    p = 0
    while n != n%d:
        if n%d != 0:
            cnt = cnt+1
        r.append(int(n%d))
        p = p+1
        n =int(n/d)  
        
    e.append(cnt)  
    r.append(n)  
    for l in range(len(r)):
        g.append(r[l]*10**l)
    A.append(g)
    g =[]




for k in range(len(e)):
    print(end ='\n')
    print(e[k] ,end = '\n' )
    for p in range(len(A[k])):
        if A[k][p] != 0:
            print(A[k][p],end = ' ')