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:
import sys
input = sys.stdin.readline


def inp():
    return(int(input()))


def inlt():
    return(list(map(int, input().split())))


def insr():
    s = input()
    return(list(s[:len(s) - 1]))


def invr():
    return(map(int, input().split()))


def pat(n):
    return n*((3*n)+1)//2


def foo():
    x = inp()
    mod = 10
    lst = []
    lst1 = []
    while x != 0:
        st = x % mod
        lst.append(st)
        x -= st
        mod = mod*10
    for item in lst:
        if item == 0:
            continue
        else:
            lst1.append(item)
    print(len(lst1))
    for i in range(len(lst1)-1):
        print(lst1[i], end=" ")
    print(lst1[-1])


if __name__ == '__main__':
    t = inp()
    for i in range(t):
        foo()