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:
t=int(input())
while t!=0:
    t-=1
    k=0
    a1=0
    b1=0
    c1=0
    d1=0
    n=int(input())
    a=n%10
    if a!=0:
          k+=1; a1=a
    b=n//10%10
    if b!=0:
          k+=1; b1=10*b
    c=n//100%10
    if c!=0:
          k+=1; c1=100*c
    d=n//1000 
    if d!=0:
          k+=1; d1=1000*d
    print(k)
    
    if a1!=0:
          print(a1,end=" ")
    if b1!=0:
          print(b1,end=" ")
    if c1!=0:
          print(c1,end=" ")
    if d1!=0:
          print(d1,end=" ")
    print()