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:
from sys import setrecursionlimit
setrecursionlimit(int(10e5))

def find(s, sm, tb, pred):
    if s == 0:
        return 0

    if s in tb:
        return tb[s]

    tb[s] = float('inf')
    for i in range(len(sm) - 1, -1, -1):
        if sm[i] > s: continue
        rs = find(s - sm[i], sm, tb, pred) + 1 
        if tb[s] > rs:
            tb[s] = rs
            pred[s] = sm[i]
    
    return tb[s]

t = int(input())
tb = {}
pred = {0:0}
sm = []
for i in range(1, 10):
    for j in range(5):
        sm.append(i * 10 ** j)
for _ in range(t):
    s = int(input())
    find(s, sm, tb, pred)
    print(tb[s])
    o = ''
    while pred[s] > 0:
        o += str(pred[s]) + ' '
        s = s - pred[s] 
    print(o)