Paint the Middle
Description
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.
Input
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.
Output
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.
Samples
7
1 2 1 2 7 4 7
2
13
1 2 3 2 1 3 3 4 5 5 5 4 7
7
Note
In the first test, it is possible to apply the following operations in order:
