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):
    n=int(input())
    s=str(n)
    l=[]
    for i in s:
        l.append(i)
    z=len(l)
    if(n==10 or n==20 or n==30 or n==40 or n==50 or n==60 or n==70 or n==80 or n==90 or n==10**z):
        print(1)
        print(n)
    else:
        l2=[]
        l3=l[::-1]
        for i in range(len(l3)):
            z=int(l3[i])*(10**i)
            l2.append(z)
        #print(l2)
        l4=[i for i in l2 if i!=0]
        print(len(l4))
        print(*l4)
    t=t-1