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:
#!/usr/bin/python3

import getopt
import sys
import math

if __name__ == "__main__":
    onlyCase = -1
    verbose = False
    
    try:
         opts, args = getopt.getopt(sys.argv[1:], "vc:",
                                   ["case="])
    except getopt.GetoptError as err:
        print (str(err)) 
        sys.exit(2)

    for o, a in opts:
        if o in ("-c", "--case"):
            onlyCase = int(a)
        elif o  == "-v":
            verbose = True
        else: sys.exit()

    
    ncases = int(input())
    for c in range(1, ncases + 1):
        N = int(input())
        
        if onlyCase != -1 and onlyCase != c:
            continue

        s = []
        c = 0
        while N > 0:
            r = N % 10
            if r > 0:
                s.append(r*(10**c))
            N = N // 10
            c += 1

        print(len(s))
        print(' '.join(map(str,s)))