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 $i$ ($1 \le i \le N$).

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

2

• Initially, we have A=(1,5,3,2,5,2,3,1).
• After replacing every occurrence of 3 in A with 2, we have A=(1,5,2,2,5,2,2,1).
• After replacing every occurrence of 2 in A with 5, we have A=(1,5,5,5,5,5,5,1).

In this way, we can make A a palindrome in two operations, which is the minimum needed.

0

A may already be a palindrome in the beginning.