#include <bits/stdc++.h>
const int MAX_MEM = 1e8;
int mpos = 0;
char mem[MAX_MEM];
inline void *operator new(size_t n) {
  assert((mpos += n) <= MAX_MEM);
  return (void *)(mem + mpos - n);
}
inline void operator delete(void *) noexcept {}
using namespace std;
void solve() {}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  int counter = 0;
  int x;
  cin >> x;
  if (x == 1) {
    counter++;
    x = -1;
  } else {
    x++;
  }
  int cur = x;
  int ans = cur;
  for (int i = 1; i < n; i++) {
    cin >> x;
    if (x == 0) {
      x = 1;
    } else {
      x = -1;
      counter++;
    }
    cur = max(cur + x, x);
    ans = max(ans, cur);
  }
  cout << ans + counter;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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.

### Response

```cpp
#include <bits/stdc++.h>
const int MAX_MEM = 1e8;
int mpos = 0;
char mem[MAX_MEM];
inline void *operator new(size_t n) {
  assert((mpos += n) <= MAX_MEM);
  return (void *)(mem + mpos - n);
}
inline void operator delete(void *) noexcept {}
using namespace std;
void solve() {}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  int counter = 0;
  int x;
  cin >> x;
  if (x == 1) {
    counter++;
    x = -1;
  } else {
    x++;
  }
  int cur = x;
  int ans = cur;
  for (int i = 1; i < n; i++) {
    cin >> x;
    if (x == 0) {
      x = 1;
    } else {
      x = -1;
      counter++;
    }
    cur = max(cur + x, x);
    ans = max(ans, cur);
  }
  cout << ans + counter;
}

```