Polycarp's New Job
Contest: Educational Codeforces Round 58 (Rated for Div. 2)
Difficulty rating: 1500
Tags: implementation

Polycarp has recently got himself a new job. He now earns so much that his old wallet can't even store all the money he has.

Berland bills somehow come in lots of different sizes. However, all of them are shaped as rectangles (possibly squares). All wallets are also produced in form of rectangles (possibly squares).

A bill $$$x \times y$$$ fits into some wallet $$$h \times w$$$ if either $$$x \le h$$$ and $$$y \le w$$$ or $$$y \le h$$$ and $$$x \le w$$$. Bills can overlap with each other in a wallet and an infinite amount of bills can fit into a wallet. That implies that all the bills Polycarp currently have fit into a wallet if every single one of them fits into it independently of the others.

Now you are asked to perform the queries of two types:

1. $$$+~x~y$$$ — Polycarp earns a bill of size $$$x \times y$$$;
2. $$$?~h~w$$$ — Polycarp wants to check if all the bills he has earned to this moment fit into a wallet of size $$$h \times w$$$.

It is guaranteed that there is at least one query of type $$$1$$$ before the first query of type $$$2$$$ and that there is at least one query of type $$$2$$$ in the input data.

For each query of type $$$2$$$ print "YES" if all the bills he has earned to this moment fit into a wallet of given size. Print "NO" otherwise.

Input format:
The first line contains a single integer $$$n$$$ ($$$2 \le n \le 5 \cdot 10^5$$$) — the number of queries.

Each of the next $$$n$$$ lines contains a query of one of these two types:

1. $$$+~x~y$$$ ($$$1 \le x, y \le 10^9$$$) — Polycarp earns a bill of size $$$x \times y$$$;
2. $$$?~h~w$$$ ($$$1 \le h, w \le 10^9$$$) — Polycarp wants to check if all the bills he has earned to this moment fit into a wallet of size $$$h \times w$$$.

It is guaranteed that there is at least one query of type $$$1$$$ before the first query of type $$$2$$$ and that there is at least one query of type $$$2$$$ in the input data.

Output format:
For each query of type $$$2$$$ print "YES" if all the bills he has earned to this moment fit into a wallet of given size. Print "NO" otherwise.

Constraints:
Time limit: 3.0 s
Memory limit: 256.0 MB

Note:
The queries of type $$$2$$$ of the example:

1. Neither bill fits;
2. Both bills fit (just checking that you got that bills can overlap);
3. Both bills fit (both bills are actually the same);
4. All bills fit (too much of free space in a wallet is not a problem);
5. Only bill $$$1 \times 5$$$ fit (all the others don't, thus it's "NO").

Example input:
9
+ 3 2
+ 2 3
? 1 20
? 3 3
? 2 3
+ 1 5
? 10 10
? 1 5
+ 1 1

Example output:
NO
YES
YES
YES
NO

Editorial:
Let's find the smallest wallet to fit all bills. One its side is the maximum side of any bill. Now we orient the bills in such a way that their longer side is put against this side of the wallet. The second side of the wallet is the maximum of the other sides. More formally, for set of bills $$$(a_1, b_1)$$$, $$$(a_2, b_2)$$$, ... ($$$a_i \le b_i$$$ for each $$$i$$$), the minimum wallet is ($$$max~a_i$$$, $$$max~b_i$$$).
The minimum wallet fits all sufficient wallets.
So the solution is maintaining the maximum of all $$$a_i$$$ and $$$b_i$$$ and checking if $$$h \ge a_i$$$ and $$$w \ge b_i$$$ ($$$h \le w$$$).
Choose your i/o functions wisely.
Overall complexity: $$$O(n)$$$.