You are given an array $$$a$$$ of $$$n$$$ integers, where all elements except for at most one are equal to $$$-1$$$ or $$$1$$$. The remaining element $$$x$$$ satisfies $$$-10^9 \le x \le 10^9$$$.

Find all possible sums of subarrays of $$$a$$$, including the empty subarray, whose sum is defined as $$$0$$$. In other words, find all integers $$$x$$$ such that the array $$$a$$$ has at least one subarray (possibly empty) with sum equal to $$$x$$$. A subarray is a contiguous subsegment of an array.

Output these sums in ascending order. Each sum should be printed only once, even if it is achieved by multiple subarrays.

Input format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Then, $$$t$$$ test cases follow.

Each test case consists of two lines:

- The first line contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of the array.
- The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$) — the elements of the array $$$a$$$. In the array $$$a$$$, there is at most one element that is neither $$$1$$$ nor $$$-1$$$.

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, output two lines:

- In the first line, print a single integer — the number of distinct subarray sums.
- In the second line, print these sums in ascending order.

Each sum should be printed only once, even if it is produced by multiple subarrays.
Example Input 0:
5
5
1 -1 10 1 1
5
-1 -1 -1 -1 -1
2
-1 2
2
7 1
3
1 4 -1

Example Output 0:
8
-1 0 1 2 9 10 11 12 
6
-5 -4 -3 -2 -1 0 
4
-1 0 1 2 
4
0 1 7 8 
6
-1 0 1 3 4 5

Notes:
Let's define $$$a[i,j]$$$ as the subarray of $$$a$$$ from position $$$i$$$ to position $$$j$$$.

Consider the first test case of the example:

- $$$-1$$$ is produced by $$$a[2,2]$$$;
- $$$0$$$ is produced by the empty subarray;
- $$$1$$$ is produced by $$$a[4,4]$$$;
- $$$2$$$ is produced by $$$a[4,5]$$$;
- $$$9$$$ is produced by $$$a[2,3]$$$;
- $$$10$$$ is produced by $$$a[1,3]$$$;
- $$$11$$$ is produced by $$$a[3,4]$$$;
- $$$12$$$ is produced by $$$a[3,5]$$$.

Example input:
5
5
1 -1 10 1 1
5
-1 -1 -1 -1 -1
2
-1 2
2
7 1
3
1 4 -1


Example output:
8
-1 0 1 2 9 10 11 12 
6
-5 -4 -3 -2 -1 0 
4
-1 0 1 2 
4
0 1 7 8 
6
-1 0 1 3 4 5