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(''))

def round(sn,out,n):
    for a in range(len(sn)):
        if sn[-(a+1)] != '0':
            out.append(''.join(sn[-(a+1):]))
            n -= int(out[-1])
            #print('ok',sn[-(a+1)],out,n,sn[-(a+1):])
            return n

def solve(n):
    out = []
    while n!=0:
        sn = list(str(n))
        n = round(sn,out,n)
    return out

o=[]
for a in range(T):
    o.append(solve(int(input(''))))
for a in o:
    print(len(a))
    print(' '.join(a))