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:
def main():
    t = int(input())
    for i in range(t):
        solve()


def solve():
    n = input()
    ln = len(n)
    m = int(n)
    k = 0
    a = []
    zero_at = []
    for i in range(ln):
        a.append(int(n[ln-i-1]))
        if m % 10 != 0:
            k+=1
            zero_at.append(i)
        m //= 10
    print(k)
    for i in range(ln):
        if a[i]!=0:
            print(a[i], end="")
            for j in range(i):
                print(0, end="")
            print(" ")


if __name__ == '__main__':
    main()