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C. Paint the Middle

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

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.

Examples

Input

7 1 2 1 2 7 4 7

Output

2

Input

13 1 2 3 2 1 3 3 4 5 5 5 4 7

Output

7

Note

In the first test, it is possible to apply the following operations in order:

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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