Segment Operations with Reversal and Range Maximum Query

You are given a sequence of length \( N \) where initially every element is 0. You need to handle \( Q \) operations on the sequence. There are three types of operations:

• Type 1: For given indices \( L \) and \( R \) and an integer \( V \), add \( V \) to every element in the segment \( [L, R] \). This can be denoted as \( a_i = a_i + V \) for every \( i \) where \( L \leq i \leq R \).
• Type 2: For given indices \( L \) and \( R \), reverse the segment \( [L, R] \). For example, the sequence 1 2 3 4 becomes 4 3 2 1 when the entire segment is reversed.
• Type 3: For given indices \( L \) and \( R \), output the maximum value in the segment \( [L, R] \).

You are to process the \( Q \) operations in order and output the result for each type 3 query.

inputFormat

The first line contains two integers \( N \) and \( Q \), where \( N \) is the length of the sequence and \( Q \) is the number of operations.

Each of the following \( Q \) lines describes an operation in one of the following formats:

• For type 1: 1 L R V
• For type 2: 2 L R
• For type 3: 3 L R

Note that the sequence is 1-indexed and initially all elements are 0.

outputFormat

For each operation of type 3, output a single line containing the maximum value in the segment \( [L, R] \).

sample

5 5
1 1 5 3
3 1 5
2 2 4
3 1 5
3 2 4

3
3
3