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 $T$. ### Constraints - $1 \leq N \leq 5 \times 10^5$ - $1 \leq Q \leq 10^5$ - $S$ 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.

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 $c=2$.