You are given n ($1$ $\le$ $n$ $\le$ $300000$) queries. Each query is one of $3$ types:
1. add pair ($a$, $b$) to the set. ($-10^9$ $\le$ $a, b$ $\le$ $10^9$)
2. remove a pair added in query $index$ (All queries are numbered with integers from $1$ to $n$).
3. For a given integer $A$ find the maximal value $a·A + b$ over all pairs ($a$, $b$) from the set. ($-10^9$ $\le$ $A$ $\le$ $10^9$). It is guaranteed that the set of pair will not be *empty*.
INPUT.
The first line contains integer $n$ ($1$ $\le$ $n$ $\le$ $3·10^5$) - the number of queries.
Each of next $n$ lines starts with integer $op$ ($1$ $\le$ $op$ $\le$ $3$) - the type of query.
OUTPUT
For each query of $3$ type print on a separate line the maximal value of $a·A + b$. It is guaranteed that the set of pair will not be *empty*.
1. query of 1 type add pair -1000000000 0 in set.
2. query of 3 type with A = 1000000000 in set we have only pair from 1 query so answer is -1000000000000000000
3. query of 1 type add pair -1000000000 1 in set.
4. query of 3 type with A = 1000000000 in set not we have pair from 1 and 3 queries and maximum value is -999999999999999999 which is reachable by pair from 3 query.