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C - Max - Min Query

Score : $300$ points

Problem Statement

We have a multiset of integers $S$, which is initially empty.

Given $Q$ queries, process them in order. Each query is of one of the following types.

• 1 x: Insert an $x$ into $S$.

• 2 x c: Remove an $x$ from $S$ $m$ times, where $m = \mathrm{min}(c,($ the number of $x$'s contained in $S))$.

• 3 : Print $($ maximum value of $S)-($ minimum value of $S)$. It is guaranteed that $S$ is not empty when this query is given.

Constraints

• $1 \leq Q \leq 2\times 10^5$
• $0 \leq x \leq 10^9$
• $1 \leq c \leq Q$
• When a query of type 3 is given, $S$ is not empty.
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$Q$

$\mathrm{query}_1$

$\vdots$

$\mathrm{query}_Q$

$\mathrm{query}_i$, which denotes the $i$-th query, is in one of the following formats:

``` $1$ $x$ ``` ``` $2$ $x$ $c$ ``` ``` $3$ ```

Output

Print the answers for the queries of type 3 in the given order, separated by newlines.

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8
1 3
1 2
3
1 2
1 7
3
2 2 3
3

1
5
4

The multiset $S$ transitions as follows.

• $1$-st query: insert $3$ into $S$. $S$ is now $\lbrace 3 \rbrace$.
• $2$-nd query: insert $2$ into $S$. $S$ is now $\lbrace 2, 3 \rbrace$.
• $3$-rd query: the maximum value of $S = \lbrace 2, 3\rbrace$ is $3$ and its minimum value is $2$, so print $3-2=1$.
• $4$-th query: insert $2$ into $S$. $S$ is now $\lbrace 2,2,3 \rbrace$.
• $5$-th query: insert $7$ into $S$. $S$ is now $\lbrace 2, 2,3, 7\rbrace$.
• $6$-th query: the maximum value of $S = \lbrace 2,2,3, 7\rbrace$ is $7$ and its minimum value is $2$, so print $7-2=5$.
• $7$-th query: since there are two $2$'s in $S$ and $\mathrm{min(2,3)} = 2$, remove $2$ from $S$ twice. $S$ is now $\lbrace 3, 7\rbrace$.
• $8$-th query: the maximum value of $S = \lbrace 3, 7\rbrace$ is $7$ and its minimum value is $3$, so print $7-3=4$.

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4
1 10000
1 1000
2 100 3
1 10

If the given queries do not contain that of type $3$, nothing should be printed.