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 Fri May 22 01:12:29 2020

@author: user
"""
#1) inp — For taking integer inputs.
#
#2) inlt — For taking List inputs.
#
#3) insr — For taking string inputs. Actually it returns a List of Characters, instead of a string, which is easier to use in Python, because in Python, Strings are Immutable.
#
#4) invr — For taking space seperated integer variable inputs.

import sys
input = sys.stdin.readline
output=sys.stdout

############ ---- Input Functions ---- ############
def inp():
    return(int(input()))
def inlt():
    return(list(map(int,input().split())))
def insr():
    s = input()
    return(list(s[:len(s) - 1]))
def invr():
    return(map(int,input().split()))

def solve(n):
    list1=[]
    count=0
    while(n!=0):
        rem=n%10
        n=n//10
        rem*=pow(10,count)
        if(rem!=0):
            list1.append(str(rem))
        count+=1
    return(list1)


n=inp()
for i in range(n):
    res=solve((inp()))
    length=len(res)
    output.write(str(length)+'\n')
    output.write(' '.join(res)+'\n')


#10
#
#
#2
#5000 9
#1
#7 
#4
#800 70 6 9000 
#1
#10000 
#1
#10