**Time limit:**1.00 s**Memory limit:**512 MB

**Input**

The first input line has a bit string consisting 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 $x_1,x_2,\ldots,x_m$ describing 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`

.