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.