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:
for _ in range(int(input())):
    a=input()
    length=len(a)
    b=int(a)
    res=[]
    res[:0]=a
    flag=False
    for i in range(len(res)):
        if i==0:
            continue
        elif res[i]!="0":
            flag=True
            break
    count=1
    count1=0
    arr=[]
    if flag==True:
        i=0
        res.reverse()
        while i<length:
            # print(res[i],count)
            c=int(res[i])
            c=c*count
            if c>0:
                arr.append(c)
            else:
                count1=count1+1
            count=count*10
            i=i+1
        print(length-count1)
        print(*arr)
    else:
        print("1")
        print(b)