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:
list1=[]
for i in range(1,11):
    list1.append(i)
arr=list1
var=10
for i in range(0,10):
    for j in range(0,10):
        tmp=var*list1[j]
        arr.append(tmp)
    var=var*10
num=int(input())
for i in range(0,num):
    final=[]
    count=0
    n=int(input())
    while(n>0):
        for i in range(0,len(arr)):
            if(arr[i]>n):
                final.append(arr[i-1])
                n=n-arr[i-1]
                count+=1
                break
    print(count)
    print(*final)