Problem Statement

You are given a sequence of $N$ positive integers: $A=(A_1,A_2, \dots A_N)$. You can do the operation below zero or more times. At least how many operations are needed to make $A$ a palindrome?

• Choose a pair $(x,y)$ of positive integers, and replace every occurrence of $x$ in $A$ with $y$.

Here, we say $A$ is a palindrome if and only if $A_i=A_{N+1-i}$ holds for every $i$ ($1 \le i \le N$).

Constraints

• All values in input are integers.
• $1 \le N \le 2 \times 10^5$
• $1 \le A_i \le 2 \times 10^5$

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

Print the answer as an integer.