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 sys import stdin,stdout
from itertools import combinations
from collections import defaultdict,Counter
import math
 
def listIn():
    return list((map(int,stdin.readline().strip().split())))
 
def stringListIn():
    return([x for x in stdin.readline().split()])
    
def intIn():
    return (int(stdin.readline()))
 
def stringIn():
    return (stdin.readline().strip())
    
    
 
if __name__=="__main__":
    t=int(input())
    while(t>0):
        t-=1
        n=int(input())
        s=str(n)
        li=[]
        c=len(s)-1
        for st in s:
            if st!='0':
                num=int(st)*10**c
                li.append(num)
            c-=1
        
        print(len(li))
        print(*li)