Problem3392--Flipping Game

3392: Flipping Game

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Iahub got bored, so he invented a game to be played on paper.

He writes n integers a1,a2,...,an. 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 ak 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.

Input

The first line of the input contains an integer n (1≤n≤100). In the second line of the input there are n integers: a1,a2,...,an. It is guaranteed that each of those n values is either 0 or 1.

Output

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

Examples
Input
5
1 0 0 1 0
Output
4
Input
4
1 0 0 1
Output
4
Note

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.

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