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.


-----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:

Difficulty: HARD

Solutions:
I = lambda : [int(i) for i in input().split()]
n = int(input())
A = I()
a = {x: i for (i, x) in enumerate(A)}
(w, v, u) = (0, 0, 0)
for (i, x) in enumerate(A):
	w = max(w, a[x])
	if v > i:
		u += 1
	else:
		v = w
print(u)


n = int(input())
a = [int(i) for i in input().split()]
last = {x: i for (i, x) in enumerate(a)}
(lastest, covered, ans) = (0, 0, 0)
for (i, x) in enumerate(a):
	lastest = max(lastest, last[x])
	if covered > i:
		ans += 1
	else:
		covered = lastest
print(ans)