Binary Sequence Transformation and Query

You are given a binary sequence of length $n$ (indexed from $0$) that consists of digits $0$ and $1$. You need to process $m$ operations. There are five types of operations:

1. 0 l r: Set all numbers in the interval $[l,r]$ to $0$.
2. 1 l r: Set all numbers in the interval $[l,r]$ to $1$.
3. 2 l r: Invert all numbers in the interval $[l,r]$ (i.e. change every $0$ to $1$ and every $1$ to $0$).
4. 3 l r: Query the total number of $1$'s in the interval $[l,r]$.
5. 4 l r: Query the maximum number of consecutive $1$'s in the interval $[l,r]$.

For each query operation (types 3 and 4), you must output the corresponding answer.

Note: All formulas are given in LaTeX format (e.g. $[l, r]$, $0$, $1$).

inputFormat

The first line contains two integers $n$ and $m$, where $n$ is the length of the binary sequence and $m$ is the number of operations.
The second line contains a binary string of length $n$ (each character is either '0' or '1').
Each of the next $m$ lines contains an operation in one of the following formats: \

• 0 l r\
• 1 l r\
• 2 l r\
• 3 l r\
• 4 l r
  
  Here, $l$ and $r$ ($0 \le l \le r < n$) denote the indices of the interval.

outputFormat

For each query operation (operations of type 3 and 4), output the answer on a new line. For a type 3 query, output the total number of $1$'s in the specified interval. For a type 4 query, output the maximum number of consecutive $1$'s in the interval.

sample

5 6
10101
3 0 4
4 0 4
2 1 3
3 1 3
0 0 1
4 0 4

3
1
2
2