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?

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$

Output

Print the answer.

Constraints

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

Sample Input 1

4
0 1 1 0

Sample Output 1

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.

Sample Input 2

5
0 0 0 0 0

Sample Output 2

6

Sample Input 3

6
0 1 0 1 0 1

Sample Output 3

3

见题面 Input 部分

见题面 Output 部分