# Problem C

Töflur

Languages
en
is
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

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 |