A14796 | Paint the Middle

You are given $n$ elements numbered from $1$ to $n$ , the element $i$ has value $a_i$ and color $c_i$ , initially, $c_i = 0$ for all $i$ .

The following operation can be applied:

- Select three elements $i$ , $j$ and $k$ ( $1 \leq i < j < k \leq n$ ), such that $c_i$ , $c_j$ and $c_k$ are all equal to $0$ and $a_i = a_k$ , then set $c_j = 1$ .

Find the maximum value of $\sum\limits_{i=1}^n{c_i}$ that can be obtained after applying the given operation any number of times.

The first line contains an integer $n$ ( $3 \leq n \leq 2 \cdot 10^5$ ) — the number of elements.

The second line consists of $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \leq a_i \leq n$ ), where $a_i$ is the value of the $i$ -th element.

Print a single integer in a line — the maximum value of $\sum\limits_{i=1}^n{c_i}$ that can be obtained after applying the given operation any number of times.