Problem Statement

$N$ plates are arranged in a straight line from left to right. Let us call the $i$-th plate from the left $(1\le i\le N)$ plate $i$. Initially, all plates are placed face-up, and no plates have takoyaki (octopus dumplings) on them.

Process a total of $Q$ queries of the following three types:

• Type $1$: You are given integers $L,R,X$. For $i=L,L+1,\ldots,R$, if plate $i$ is placed face-up, place $X$ takoyaki on plate $i$.
• Type $2$: You are given integers $L,R$. For $i=L,L+1,\ldots,R$, if there is at least one takoyaki on plate $i$, eat all the takoyaki on plate $i$. Flip plate $i$ (if the plate is placed face-up, place it face-down; otherwise, place it face-up).
• Type $3$: You are given integers $L,R$. Print the maximum number of takoyaki on one plate among plates $L,$ $L+1,\ldots,$ $R$.

Constraints

• $1\le N\le2\times10 ^ 5$
• $1\le Q\le2\times10 ^ 5$
• In all queries, $1\le L\le R\le N$.
• In type $1$ queries, $1\le X\le10 ^ 9$.
• There is at least one type $3$ query.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N Q
\mathrm{query} _ 1
\mathrm{query} _ 2
\vdots
\mathrm{query} _ Q

Here, $\mathrm{query} _ i$ represents the $i$-th $(1\le i\le Q)$ query and is given in one of the following formats:

t L R X

t L R

These indicate that the $i$-th query is of type $t$ and the given integers are $L,R,X$ or $L,R$. Type $1$ queries are given in the former format, and other queries are given in the latter format.

Output

Let $q$ be the number of type $3$ queries. Print $q$ lines. The $i$-th line $(1\le i\le q)$ should contain the answer to the $i$-th type $3$ query from the beginning.