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:
# Je déteste que j'aime que je déteste

########## A. I_love_%username% ############
# n, k = map(int, inputt().split())
# time_left = (4*60) - k
# r,i = 0, 1
# while (5 * ((i*(i+1))/2)) < time_left and i <= n:
#     r += 1
#     i += 1
# print(r)


t = int(input())

for _ in range(t):
    r = []
    rr = 0
    n = int(input())
    if n >= 10000:
        r.append(n//10000*10000)
        n = n % 10000
        rr +=1
    if n >= 1000:
        r.append(n//1000*1000)
        n = n % 1000
        rr += 1
    if n >= 100:
        r.append(n//100*100)
        n = n % 100
        rr += 1
    if n >= 10:
        r.append(n//10*10)
        n = n % 10
        rr += 1
    if n < 10 and n > 0:
        r.append(n)
        rr += 1
    print(rr)
    print(' '.join(map(str, r)))