Flipping Game

题意翻译

小I有些无聊，所以他发明了一个在纸上玩的游戏。 他写下了n个整数a1,a2,a3,a4......an，每个都是0或1中的一个。他被允许做如下的**一次**操作：他选择一个起点i，一个终点j，保证1<=i<=j<=n，然后将区间中的每一个数**翻转**。**翻转指将ax的值设定为1-ax。** 问：翻转一次后，最多有几个1. ————Translated by Mr.Kevin

题目描述

Iahub got bored, so he invented a game to be played on paper. He writes $ n $ integers $ a_{1},a_{2},...,a_{n} $ . Each of those integers can be either 0 or 1. He's allowed to do exactly one move: he chooses two indices $ i $ and $ j $ ( $ 1<=i<=j<=n $ ) and flips all values $ a_{k} $ for which their positions are in range $ [i,j] $ (that is $ i<=k<=j $ ). Flip the value of $ x $ means to apply operation $ x=1 $ - $ x $ . The goal of the game is that after exactly one move to obtain the maximum number of ones. Write a program to solve the little game of Iahub.

输入输出格式

输入格式

The first line of the input contains an integer $ n $ ( $ 1<=n<=100 $ ). In the second line of the input there are $ n $ integers: $ a_{1},a_{2},...,a_{n} $ . It is guaranteed that each of those $ n $ values is either 0 or 1.

输出格式

Print an integer — the maximal number of 1s that can be obtained after exactly one move.

输入输出样例

输入样例 #1

5
1 0 0 1 0

输出样例 #1

4

输入样例 #2

4
1 0 0 1

输出样例 #2

4

说明

In the first case, flip the segment from 2 to 5 $ (i=2,j=5) $ . That flip changes the sequence, it becomes: \[1 1 1 0 1\]. So, it contains four ones. There is no way to make the whole sequence equal to \[1 1 1 1 1\]. In the second case, flipping only the second and the third element $ (i=2,j=3) $ will turn all numbers into 1.