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:
#code
import sys
import math as mt
#input=sys.stdin.buffer.readline
t=int(input())
#tot=0


for __ in range(t):
    #n=int(input())      
    #l=list(map(int,input().split()))  
    #n,m=map(int,input().split())            
    #l=list(map(int,input().split()))
    s=input()
    if len(s)==1:
        print(1)
        print(s)
    else:
        ans1=''
        ans2=''
        ans3=''
        ans4=''
        k=0
        z=0
        #print(1,s)
        for i in range(len(s)-1,-1,-1):
            if s[i]!='0':
                k+=1
                #print(111,k,z)
                if k==1:
                    ans1+=s[i]
                    for j in range(z):
                        ans1+='0'
                if k==2:
                    ans2+=s[i]
                    for j in range(z):
                        ans2+='0'
                if k==3:
                    ans3+=s[i]
                    for j in range(z):
                        ans3+='0'
                if k==4:
                    ans4+=s[i]
                    for j in range(z):
                        ans4+='0'
            z+=1        
            
        l=[]        
        l.append(ans1)
        l.append(ans2)
        l.append(ans3)
        l.append(ans4)
        print(k)
        for i in range(k):
            print(l[i],end=" ")
        print()