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())

numArr = []


# define the isRound() function
def isRound(num):
    num = str(num)
    for i in range(1, len(num)):
        if num[i] != '0':
            return False
    return True


for i in range(t):
    numArr.append(int(input()))


for i in range(t):
    if isRound(numArr[i]):
        count = 1
        print(count)
        print(numArr[i])
    else:
        count = 1
        roundNumsStr = ""
        while isRound(numArr[i]) == False:
            strNum = str(numArr[i])
            numToSub = ""
            numToSub += strNum[0]
            for j in range(1, len(strNum)):
                numToSub += "0"
            numToSub = int(numToSub)
            roundNumsStr += str(numToSub) + " "
            numArr[i] = numArr[i] - numToSub
            count += 1
        print(count)
        print(roundNumsStr + str(numArr[i]))