Lena is a programmer. She got a task to solve at work.

There is an empty set of pairs of integers and *n* queries to process. Each query is one of three types:
 1.  Add a pair (*a*, *b*) to the set. 1.  Remove a pair added in the query number *i*. All queries are numbered with integers from 1 to *n*. 1.  For a given integer *q* find the maximal value *x*·*q* + *y* over all pairs (*x*, *y*) from the set. 
Help Lena to process the queries.
The first line of input contains integer *n* (1 ≤ *n* ≤ 3·10<sup class="upper-index">5</sup>) — the number of queries.

Each of the next *n* lines starts with integer *t* (1 ≤ *t* ≤ 3) — the type of the query.

A pair of integers *a* and *b* ( - 10<sup class="upper-index">9</sup> ≤ *a*, *b* ≤ 10<sup class="upper-index">9</sup>) follows in the query of the first type.

An integer *i* (1 ≤ *i* ≤ *n*) follows in the query of the second type. It is guaranteed that *i* is less than the number of the query, the query number *i* has the first type and the pair from the *i*-th query is not already removed.

An integer *q* ( - 10<sup class="upper-index">9</sup> ≤ *q* ≤ 10<sup class="upper-index">9</sup>) follows in the query of the third type.
none
7
3 1
1 2 3
3 1
1 -1 100
3 1
2 4
3 1
EMPTY SET
5
99
5
5
1 -1 2
1 0 -1
2 2
1 -2 -1
3 -1
3
3
1 -2 2
1 -3 0
3 -1
4
3
1 0 -2
1 2 -2
3 1
0
3
1 -1 0
1 -1 1
3 -2
3
10
3 -10
1 6 -2
1 8 -3
2 3
1 -6 -3
2 2
3 6
3 4
2 5
1 3 -9
EMPTY SET
-39
-27
10
3 0
3 0
3 0
3 0
1 0 0
1 0 0
1 0 0
3 0
3 0
2 6
EMPTY SET
EMPTY SET
EMPTY SET
EMPTY SET
0
0
1
3 840
EMPTY SET
4
1 -1000000000 0
3 1000000000
1 -1000000000 1
3 1000000000
-1000000000000000000
-999999999999999999
3
1 -1000000000 0
1 -1000000000 0
3 1000000000
-1000000000000000000
3
1 -1000000000 0
3 1000000000
2 1
-1000000000000000000
2
1 -1000000000 0
3 1000000000
-1000000000000000000
2
1 -1000000000 -7
3 1000000000
-1000000000000000007
2
1 -1000000000 -1000000000
3 1000000000
-1000000001000000000
print("_RANDOM_GUESS_1689181805.080144")# 1689181805.0801961