qarentheziz zepuence

Ryan is interested in strings consisting only of ‘(' and ‘)'. Especially, he loves balanced strings. Any balanced strings can be constructed using the following rules:

• A string “()" is balanced.
• The concatenation of two balanced strings is balanced.
• If $T$ is a balanced string, the concatenation of ‘(', $T$, and ‘)' in this order is balanced.

For example, “()()" and “(()())" are balanced strings. “)(", “)()(()" and “(" are not balanced strings.

We define Ryan's sadness for a string $T$ as the minimum number of operations required to make $T$ into a balanced string by doing the following operations in any order and any number of times.

• Add ‘)' to the beginning of $T$.
• Add ‘(' to the end of $T$.
• Swap two adjacent characters of $T$.

Ryan has a string $S$ of length $N$ consisting only of ‘(' and ‘)'. Given $Q$ queries, process them in order. There are two kinds of queries with the following formats.

• “$1$ $l$ $r$": For each character from the $l$-th to the $r$-th (including $r$-th) of $S$, if it is ‘(', replace it with ‘)'. If it is ‘)', replace it with ‘('.
• “$2$ $l$ $r$": Output the value of Ryan's sadness for the substring from the $l$-th through $r$-th characters of $S$.

The input consists of a single test case of the following format.

$N$ $Q$

$S$

$t\_1$ $l\_1$ $r\_1$

$\vdots$

$t\_Q$ $l\_Q$ $r\_Q$

The first line contains two integers $N$ and $Q$ ($2 ≤ N ≤ 150\\,000$, $1 ≤ Q ≤ 150\\,000$) separated by a space, which represent the length of the string $S$ and the number of queries. The following line contains the string $S$, which consists only of ‘(' and ‘)', and whose length is $N$. Each of the next $Q$ lines contains three integers $t\_i$, $l\_i$ and $r\_i$($1 ≤ t\_i ≤ 2$, $1 ≤ l\_i ≤ r\_i ≤ N$) separated by a space, which represent the $i$-th query. It is guaranteed that there is at least one query with $t\_i = 2$.

For each query in the format “$2$ $l$ $r$", print the value of Ryan's sadness, followed by a newline.