CSES Problem Set

# Bit Inversions

CSES - Bit Inversions

 Time limit: 1.00 s Memory limit: 512 MB

There is a bit string that consists of $n$ bits. Then, there are some changes that invert bits. Your task is to report, after each change, the length of the longest substring whose each bit is the same.

Input

The first input line has a bit string that consists of $n$ bits. The bits are numbered $1,2,\ldots,n$.

The next line contains an integer $m$: the number of changes.

The last line contains $m$ integers $x_1,x_2,\ldots,x_m$ which describe the changes.

Output

After each change, print the length of the longest substring whose each bit is the same.

Constraints
• $1 \le n \le 2 \cdot 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le x_i \le n$
Example

Input:
001011 3 3 2 5

Output:
4 2 3

Explanation: The bit string first becomes 000011, then 010011, and finally 010001.