Your task is to efficiently process the following types of queries:

1. Add a line $ax+b$
2. Find the maximum point in any line at position $x$

Input

The first line has an integer $n$: the number of queries.

The following $n$ lines describe the queries. The format of each line is either "1 $a$ $b$" or "2 $x$".

You may assume that the first query is of type 1.

Output

Print the answer for each query of type 2.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $-10^9 \le a,b \le 10^9$
• $0 \le x \le 10^5$

Example

Input:

6
1 1 2
2 1
2 3
1 0 4
2 1
2 3

Output:

3
5
4
5