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:
no = int(input())
li = []
li2 = []
for i in range(0,no):
    li.append(int(input()))
for i in li:
    temp = i
    tl = []
    while temp!=0:
        tl.append(temp%10)
        #print(temp)
        temp = temp//10
    #print(tl)
    temp = i
    tl2 = []
    while tl != []:
        if tl[len(tl) - 1] == 0:
            tl.pop()
        else:
            mul = tl[len(tl) - 1]* pow(10, len(tl)-1)
            tl2.append(mul)
            temp = temp - mul
            tl.pop()
    li2.append(tl2)
for i in li2:
    print(len(i))
    for j in i:
        if j != i[len(i)-1]:
            print(j, end=" ")
        else:
            print(j)