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:
from collections import deque
from collections import OrderedDict
import math
#data = sys.stdin.readlines()
import sys
import os
from io import BytesIO
import threading
import bisect


 
 
#input = sys.stdin.readline
for t in range(int(input())):
    n = str(input())
    leng = len(n)
    answers = []
    zeros = []
    countZ = 0
    for i in range(leng-1,-1,-1):     
        if n[i]!='0':
            #print(n[i])
            answers.append(int(n[i]))
            zeros.append(countZ)
        countZ+=1
    print(len(answers))
    for i in range(len(answers)):
        print(answers[i]*(10**zeros[i]), end=" ")