Score : $500$ points

Problem Statement

For a sequence $X$, let $f(X) =$ (the minimum number of elements one must modify to make $X$ a palindrome).

Given a sequence $A$ of length $N$, find the sum of $f(X)$ over all contiguous subarrays of $A$.

Here, a sequence $X$ of length $m$ is said to be a palindrome if and only if the $i$-th and the $(m+1-i)$-th elements of $X$ are equal for all $1 \le i \le m$.

Constraints

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

Input

The 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.

5
5 2 1 2 2

9

• $f(5) = 0$
• $f(2) = 0$
• $f(1) = 0$
• $f(2) = 0$
• $f(2) = 0$
• $f(5,2) = 1$
• $f(2,1) = 1$
• $f(1,2) = 1$
• $f(2,2) = 0$
• $f(5,2,1) = 1$
• $f(2,1,2) = 0$
• $f(1,2,2) = 1$
• $f(5,2,1,2) = 2$
• $f(2,1,2,2) = 1$
• $f(5,2,1,2,2) = 1$

Therefore, the sought answer is $9$.