Tricky Function

题意翻译

- 给定长度为 $n$ 的序列 $a$。 - 定义函数 $f(i,j)=(i-j)^2+g(i,j)^2$，其中 $g(i,j)$ 的计算方式如以下伪代码： ```cpp 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; } ``` - 求 $\displaystyle\min_{i\ne j}f(i,j)$。 - $2\le n\le 10^5$，$|a_i|\le 10^4$。

题目描述

Iahub 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?

输入输出格式

输入格式

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} $ ).

输出格式

Output a single integer — the value of $ min_{i≠j}  f(i,j) $ .

输入输出样例

输入样例 #1

4
1 0 0 -1

输出样例 #1

1

输入样例 #2

2
1 -1

输出样例 #2

2

题意翻译

- 给定长度为 $n$ 的序列 $a$。 - 定义函数 $f(i,j)=(i-j)^2+g(i,j)^2$，其中 $g(i,j)$ 的计算方式如以下伪代码： ```cpp 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; } ``` - 求 $\displaystyle\min_{i\ne j}f(i,j)$。 - $2\le n\le 10^5$，$|a_i|\le 10^4$。