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:
Add a pair (a,b) to the set. Remove a pair added in the query number i. All queries are numbered with integers from 1 to n. For a given integer q find the maximal value x \cdot 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 \le n \le 3 \cdot 105) - the number of queries.

Each of the next n lines starts with integer t (1 \le t \le 3) - the type of the query.

A pair of integers a and b (-109 \le a,b \le 109) follows in the query of the first type.

An integer i (1 \le i \le 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 (-109 \le q \le 109) follows in the query of the third type.

For the queries of the third type print on a separate line the desired maximal value of x \cdot q+y.

If there are no pairs in the set print "EMPTY SET".