Lena and Queries

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.
2. Remove a pair added in the query number i. All queries are numbered with integers from 1 to n.
3. 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.

Input

The first line of input contains integer n (1 ≤ n ≤ 3·105) — 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 ( - 109 ≤ a, b ≤ 109) 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 ( - 109 ≤ q ≤ 109) follows in the query of the third type.

Output

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

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

Example

Input

7 3 1 1 2 3 3 1 1 -1 100 3 1 2 4 3 1

Output

EMPTY SET 5 99 5

inputFormat

Input

The first line of input contains integer n (1 ≤ n ≤ 3·105) — 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 ( - 109 ≤ a, b ≤ 109) 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 ( - 109 ≤ q ≤ 109) follows in the query of the third type.

outputFormat

Output

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

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

Example

Input

7 3 1 1 2 3 3 1 1 -1 100 3 1 2 4 3 1

Output

EMPTY SET 5 99 5

样例

7
3 1
1 2 3
3 1
1 -1 100
3 1
2 4
3 1

EMPTY SET
                                                           5
                                                          99
                                                           5

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