Palindromic Binary Numbers ~ Multiplex Coder

We call a non-negative number

$x$ good if its binary representation is palindromic. For example, $107$ is good because its binary representation is $1101011$ which is palindromic while $10$ is not good because its binary representation is $1010$ which is not palindromic.

Recall that, a string is said to be palindromic if it reads the same backward as forward.

You are given a number $n$ . You have to express $n$ as a sum of at most $12$ good numbers. If there exist multiple answers, print any one of them.

Input Format

The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first and only line of each testcase contains a single integer $n$ .

Output Format

For each testcase, print a single integer $m$ ( $1 \leq m \leq 12$ ), denoting the number of good numbers. In the next line, print a sequence of $m$ good numbers whose sum is equal to $n$ . If there are multiple such sequences, print any of them.

Constraints

$1 \leq T \leq 1000$
$1 \leq n \leq 1000$

Sample Input 1

2
24
4

Sample Output 1

Explanation

Test case $1$ :

$21$ is good because $21 = (10101)_{2}$ which is palindromic.
$3$ is good because $3 = (11)_{2}$ which is palindromic.

Test case $2$ :

$1$ is good because $1 = (1)_{2}$ which is palindromic.

Here $()_{2}$ denotes binary representation of the number.