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 value(lw):
    str2=""
    for x in range(lw-1):
        str2+="0"
    return str2

n=input()
import math
for x in range(int(n)):
    val=input()
    arr=[]
    while len(val)!=1:
        tik=value(len(val))
        div="1"+tik
        #print("v: ",val," ",div)
        f=str(int(int(val)/int(div)))+tik
        #print(f,end=" ")
        arr.append(f)
        val2=int(val) % int(div)
        val=str(val2)
    if val!='0':
        arr.append(val)
    print(len(arr))
    for nn in arr:
        print(nn,end=" ")
    print()