Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

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D. Tricky Function

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIahub and Sorin are the best competitive programmers in their town. However, they can't both qualify to an important contest. The selection will be made with the help of a single problem. Blatnatalag, a friend of Iahub, managed to get hold of the problem before the contest. Because he wants to make sure Iahub will be the one qualified, he tells Iahub the following task.

You're given an (1-based) array *a* with *n* elements. Let's define function *f*(*i*, *j*) (1 ≤ *i*, *j* ≤ *n*) as (*i* - *j*)^{2} + *g*(*i*, *j*)^{2}. Function g is calculated by the following pseudo-code:

int g(int i, int j) {

int sum = 0;

for (int k = min(i, j) + 1; k <= max(i, j); k = k + 1)

sum = sum + a[k];

return sum;

}

Find a value *min*_{i ≠ j} *f*(*i*, *j*).

Probably by now Iahub already figured out the solution to this problem. Can you?

Input

The first line of input contains a single integer *n* (2 ≤ *n* ≤ 100000). Next line contains *n* integers *a*[1], *a*[2], ..., *a*[*n*] ( - 10^{4} ≤ *a*[*i*] ≤ 10^{4}).

Output

Output a single integer — the value of *min*_{i ≠ j} *f*(*i*, *j*).

Examples

Input

4

1 0 0 -1

Output

1

Input

2

1 -1

Output

2

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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