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:
# cook your dish here
MOD =  1000000007
#import time
#import heapq
#import math
#import string
#import bisect


def solve(n):
    ans = []
    i = 1
    while n!=0:
        val = (n%10)*(10**(i-1))
        if val!=0:
            ans.append(val)
        n = n//10
        i+=1
    print(len(ans))
    print(*ans,sep=" ")
     
            
for i in range(int(input())):
    #x,y,l,r= map(int,input().split())
    #n,k= map(int,input().split())
    n = int(input())
    #a = list(map(int,input().split()))
    #b = list(map(int,input().split()))
    #l,r= map(int,input().split())
    #n = int(input())
    #s = input()
    #sa = list(map(str,input().split()))
    #b = list(map(int,input().split()))
    #st = time.process_time()
    solve(n)
    #print(s)
    #pt = solve(s)
    #print(pt)
    #print("yes" if pt==1 else "no")
    #print("Linear : ",time.process_time() - st)