Description

Input

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.

The first line of each testcase contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$).

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^9$).

The sum of $n$ over all testcases doesn't exceed $2 \cdot 10^5$.

Output

For each testcase, print the smallest number of operations required to make all elements of the array equal.

If the number of operations is less than or equal to $n$, then print the chosen $x$ for each operation in the next line. If there are multiple answers, print any of them.

4
1
10
2
4 6
6
2 1 2 1 2 1
2
0 32

0
2
2 5
1
1
6

Note

In the first testcase, all elements are already equal, so $0$ operations are required. It doesn't matter if you print an empty line afterwards or not.

In the second testcase, you can't make less than $2$ operations. There are multiple answers, let's consider the answer sequence $[2, 5]$. After applying an operation with $x = 2$, the array becomes $[\lfloor \frac{4 + 2}{2} \rfloor, \lfloor \frac{6 + 2}{2} \rfloor] = [3, 4]$. After applying an operation with $x = 5$ after that, the array becomes $[\lfloor \frac{3 + 5}{2} \rfloor, \lfloor \frac{4 + 5}{2} \rfloor] = [4, 4]$. Both elements are the same, so we are done.

In the last testcase, you can't make less than $6$ operations. Since $6$ is greater than $n$, you don't have to print them. One possible answer sequence is $[0, 0, 0, 0, 0, 0]$. We are just dividing the second element by $2$ every time and not changing the first element.