Problem Statement

There is an integer sequence $A=(A_1,A_2,\dots,A_N)$ of length $N$ consisting of $0$ and $1$. You are given $Q$ queries. The $q$-th query is as follows:

• An integer $i_q$ between $1$ and $N$ is given. Change $A_{i_q}$ to $1$ if it is $0$, and to $0$ if it is $1$.

After processing each query, find the answer to the following problem:

Consider sequences $B=(B_1,B_2,\dots,B_{|B|})$ consisting of $0$ and $1$ that satisfy the following condition:

• By performing the following operation any number of times on $B$, it can be made to match sequence $A$:
• Choose an integer $i$ between $1$ and $|B|-1$, inclusive.
  • Insert $B_i\oplus B_{i+1}$ between $B_i$ and $B_{i+1}$.

It can be proved that there always exists a

B

that satisfies the condition. Find the minimum possible value of

|B|

.

Constraints

• $3 \leq N \leq 2 \times 10^5$
• $0 \leq A_i \leq 1$
• $1 \leq Q \leq 5 \times 10^5$
• $1 \leq i_q \leq N$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N
Q
i_1
i_2
\vdots
i_Q

Output

Output the answers in a total of $Q$ lines. The $q$-th line should contain the answer to the problem after processing the $q$-th query.