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:
import math
T = int(input())
end_ans =[]
while(T>0):
    n = input()
    end_ans.append(n)
    T -= 1
T = len(end_ans)
for i in range(T):
    ans_list =[]
    n = end_ans[i]
    length = len(n)
    copy_n = int(n)
    while(copy_n>0):
        ans_list.append(copy_n%10)
        copy_n = copy_n // 10
    cnt =0
    for i in range(length):
        ans_list[i] = ans_list[i] * int(math.pow(10,i))
        if(ans_list[i]==0):
            cnt += 1
    for i in range(cnt):
        ans_list.remove(0)
    print(len(ans_list))
    for i in ans_list:
        print(i ,end=" ")
    print()