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())
for w in range(t):
    n = input()
    l = list(n)
    j = len(l)
    s = []
    for i in range(len(l)):
        j = j - 1
        if j == 0:
            x = pow(10, len(l) - 1)
            y = int(l[j])
            z = x * y
            s.append(z)
            break;
        if l[j] != '0':
            d1 = pow(10, len(l) - 1)
            d2 = pow(10, j)
            d = int(d1 / d2)
            m = int(l[j])
            t = m * d
            s.append(t)
    print(len(s))
    a = ""
    for k in range(len(s)):
        a = a + str(s[k]) + " "
    print(a)