You are given a string $S$ of length $N$ consisting of `0` and `1`. Let $S_i$ denote the $i$-th character of $S$.

Process $Q$ queries in the order they are given.  
Each query is represented by a tuple of three integers $(c, L, R)$, where $c$ represents the type of the query.

-   When $c=1$: For each integer $i$ such that $L \leq i \leq R$, if $S_i$ is `1`, change it to `0`; if it is `0`, change it to `1`.
-   When $c=2$: Let $T$ be the string obtained by extracting the $L$-th through $R$-th characters of $S$. Print the maximum number of consecutive `1`s in $T$.

The input is given from Standard Input in the following format, where $\mathrm{query}_i$ represents the $i$-th query:

```
$N$ $Q$
$S$
$\mathrm{query}_1$
$\mathrm{query}_2$
$\vdots$
$\mathrm{query}_Q$
```

Each query is given in the following format:

```
$c$ $L$ $R$
```

Let $k$ be the number of queries with $c=2$. Print $k$ lines.  
The $i$-th line should contain the answer to the $i$-th query with $c=2$.

-   $1 \leq N \leq 5 \times 10^5$
-   $1 \leq Q \leq 10^5$
-   $S$ is a string of length $N$ consisting of `0` and `1`.
-   $c \in \lbrace 1, 2 \rbrace$
-   $1 \leq L \leq R \leq N$
-   $N$, $Q$, $c$, $L$, and $R$ are all integers.

3
1
0
7

The queries are processed as follows.

• Initially, S= 1101110.
• For the first query, T= 1101110. The longest sequence of consecutive 1s in T is 111 from the 4-th character to 6-th character, so the answer is 3.
• For the second query, T= 101. The longest sequence of consecutive 1s in T is 1 at the 1-st or 3-rd character, so the answer is 1.
• For the third query, the operation changes S to 1110000.
• For the fourth query, T= 00. T does not contain 1, so the answer is 0.
• For the fifth query, the operation changes S to 1111111.
• For the sixth query, T= 1111111. The longest sequence of consecutive 1s in T is 1111111 from the 1-st to 7-th characters, so the answer is 7.