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Problem A
Töflur

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You really like playing games with your friend. You are currently playing a game where each player is given $n$ tiles with numbers on them. Each player then places the tiles down such that they form a sequence. Let $a_ j$ denote the number on the $j$-th tile in the sequence, for $j=1, 2, \dotsc , n$. The score of the sequence is then computed by adding up the squares of differences of adjacent tiles, that is

\[ \sum _{j = 1}^{n - 1} (a_ j - a_{j + 1})^2. \]

The player with the lowest score wins.

Input

The first line of the input is an integer $n$, the number of tiles you have, where $1 \leq n \leq 10^6$. The next line consists of $n$ integers each being at least one, but not larger than $10^6$.

Output

The only line of the output should contain one integer, the lowest score you can achieve by arranging your tiles optimally.

Scoring

Groups

Points

Constraints

1

15

$n = 3$

2

42

$n \leq 18$

3

43

No further constraints

Sample Input 1 Sample Output 1
9
1 2 3 1 1 2 2 3 3
2
Sample Input 2 Sample Output 2
7
4 8 7 25 95 97 6
5199

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