code_segments/segment_298.txt

[EnV - Dynasty](https://soundcloud.com/envyofficial/env-dynasty)

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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 number of red elements. Find the maximum score you can get.

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \le n \le 100$) — the length of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 1000$) — the given array.

For each test case, output a single integer: the maximum possible score you can get after coloring some elements red according to the statement.

In the first test case, you can color the array as follows: $[\color{red}{5}, 4, \color{red}{5}]$. Your score is $\max([5, 5]) + \text{size}([5, 5]) = 5+2 = 7$. This is the maximum score you can get.

In the second test case, you can color the array as follows: $[\color{red}{4}, 5, \color{red}{4}]$. Your score is $\max([4, 4]) + \text{size}([4, 4]) = 4+2 = 6$. This is the maximum score you can get.

In the third test case, you can color the array as follows: $[\color{red}{3}, 3, \color{red}{3}, 3, \color{red}{4}, 1, 2, \color{red}{3}, 4, \color{red}{5}]$. Your score is $\max([3, 3, 4, 3, 5]) + \text{size}([3, 3, 4, 3, 5]) = 5+5 = 10$. This is the maximum score you can get.