You are given an array $$$a_1, a_2, \ldots, a_n$$$ of positive integers.

You can color some elements of the array red, but there cannot be two adjacent red elements (i.e., for $$$1 \leq i \leq n-1$$$, at least one of $$$a_i$$$ and $$$a_{i+1}$$$ must not be red).

Your score is the maximum value of a red element, plus the minimum value of a red element, plus the number of red elements. Find the maximum score you can get.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the length of the array.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$) — the given array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, output a single integer: the maximum possible score you can get after coloring some elements red according to the statement.
Example Input 0:
4
3
5 4 5
3
4 5 4
10
3 3 3 3 4 1 2 3 5 4
10
17 89 92 42 29 41 92 14 70 45

Example Output 0:
12
11
12
186

Notes:
In the first test case, you can color the array as follows: $$$[\color{red}{5}, 4, \color{red}{5}]$$$. Your score is $$$\max([5, 5]) + \min([5, 5]) + \text{size}([5, 5]) = 5+5+2 = 12$$$. This is the maximum score you can get.

In the second test case, you can color the array as follows: $$$[4, \color{red}{5}, 4]$$$. Your score is $$$\max([5]) + \min([5]) + \text{size}([5]) = 5+5+1 = 11$$$. This is the maximum score you can get.

In the third test case, you can color the array as follows: $$$[\color{red}{3}, 3, \color{red}{3}, 3, \color{red}{4}, 1, 2, \color{red}{3}, 5, \color{red}{4}]$$$. Your score is $$$\max([3, 3, 4, 3, 4]) + \min([3, 3, 4, 3, 4]) + \text{size}([3, 3, 4, 3, 4]) = 4+3+5 = 12$$$. This is the maximum score you can get.

Example input:
4
3
5 4 5
3
4 5 4
10
3 3 3 3 4 1 2 3 5 4
10
17 89 92 42 29 41 92 14 70 45


Example output:
12
11
12
186