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:
# -*- coding: utf-8 -*-
"""
Created on Tue Sep  1 03:17:49 2020
1352A  Sum of Round Numbers
@author: RACHIT
"""

def check(n:int) -> list:
    if n==0:
        return []
    n=str(n)
    ans=[]
    for i in range(len(n)):
        a=int(n[i])*10**(len(n)-i-1)
        if a:
            ans.append(a)
    return ans
if __name__=="__main__":
    t=int(input())
    while(t):
        n=int(input())
        ans=check(n)
        print(len(ans))
        for i in ans:
            print(i,end=' ')
        t-=1