SOLVE
LATER
This task is really interesting so authors even decided not to spend your time on reading the statement!
Initially you have a straight line without any points on it and you need to perform three types of queries:
1 $$x$$ - add a point with an integer coordinate $$x$$. Guaranteed that there is no such point before running this query.
2 $$x$$ - delete a point with an integer coordinate $$x$$. Guaranteed that this point exists before running this query.
3 $$x$$ - define a coordinate of i-th existing point in increasing order as $$x_i$$ and number of existing points as $$n$$. You need to find $$max ( \sum_{i=1}^{n-1} |x_{p_{i+1}} - x_{p_i}| )$$ for all permutations $$p$$ of length $$n$$ where $$x_{p_1}=x$$. Guaranteed that this point exists before running this query.
Input
The first line of input contains a single integer $$q$$ $$(1 \leq q \leq 100 000)$$ - the number of queries.
Then follow $$q$$ lines. The i-th of these lines contains two integers $$type_i$$ and $$x_i$$ $$(1 \leq type_i \leq 3, 0 \leq x_i \leq 10^{9})$$.
Output
For each query of the third type print the maximum value.
Permutation for the first ask query is {3, 1, 4, 2}. It's value is 11.
Permutation for the second ask query is {3, 1, 2}. It's value is 7.