Score : $400$ points

Problem Statement

You are given an integer sequence of length $N$ consisting of $0$ and $1$: $A=(A_1,A_2,\cdots,A_N)$.

You will do the operation below exactly once.

• Choose a contiguous subsequence of $A$ and flip the elements in it: convert $0$ to $1$ and vice versa. Here, you may choose an empty subsequence, in which case the elements of $A$ do not change.

Your score will be the number of $1$'s in $A$. How many values are there that your score can take?

Constraints

• $1 \leq N \leq 3 \times 10^5$
• $0 \leq A_i \leq 1$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\cdots$ $A_N$

Output

Print the answer.

4
0 1 1 0

4

There are four possible values for your score: $0, 1, 2, 3$. For example, if you flip the $2$-nd through $4$-th elements of $A$, you will get $A=(0,0,0,1)$, for a score of $1$.

5
0 0 0 0 0

6

6
0 1 0 1 0 1

3