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 round(x):
    if x < 10:
        return [1,x]
    else:
        s = x % 10
        u = (x - s) % 100
        v = (x - s - u) % 1000
        w = (x - s - u - v) % 10000
        if x >= 1000:
            if x % 1000 == 0:
                return [1,x]
            elif x == 10000:
                return [1,x]
            elif s == 0 and u == 0:
                return [2,v,w]
            elif s == 0 and v == 0:
                return [2,u,w]
            elif u == 0 and v == 0:
                return [2,s,w]
            elif u == 0:
                return [3,s,v,w]
            elif v == 0:
                return [3,s,u,w]
            elif s == 0:
                return [3,u,v,w]
            else:
                return [4,s,u,v,w]
        elif x >= 100:
            if x % 100 == 0:
                return [1,x]
            elif u == 0:
                return [2,s,v]
            elif s == 0:
                return [2,u,v]
            else:
                return [3,s,u,v]
        elif x >= 10:
            if x % 10 == 0:
                return [1,x]
            return [2,s,u]

t = int(input())
a = []
ans = []
for i in range(t):
    a.append(input())
for i in a:
    ans.append(round(int(i)))
for i in ans:
    print(i[0])
    for j in range(1,len(i)):
        print(i[j],end = ' ')
    print()