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
class RoundNumbers:
    def __init__(self, num):
        self.num = int(num)
        self.times = 0
        self.answer = []
    
    def findSumOfRoundNumbers(self):
        runningNumber = self.num
        index = 0
        while int(math.log10(self.num)) + 1 > index:
            remainder = runningNumber % 10
            runningNumber = int(runningNumber / 10)
            if remainder > 0:
                self.answer.append(remainder * pow(10, index))
                self.times = self.times + 1
            index = index + 1 
        
        print(self.times)
        ##self.answer.reverse()
        ans = ""
        for a in self.answer:
            ans = ans + str(a) + " "
        print(ans)


if __name__ == "__main__":
    numOfRecords = input()
    numArr = []
    ##print(numOfRecords)
    for count in range(0, int(numOfRecords)):
        num = input()
        numArr.append(num)
    for num in numArr:
        rn = RoundNumbers(num)
        rn.findSumOfRoundNumbers()