Ping-Pong

题意翻译

有一个区间的集合，初始为空。当 $c<a<d$ 或 $c<b<d$ ，且 $(a,b),(c,d)$ 都在集合中时，你可以从区间 $(a,b)$ 移动到 $(c,d)$。你需要支持下面的操作： - 1 x y，加入一个新区间 $(x,y)$。保证加入的区间长度严格单调递增。 - 2 a b，询问是否能从第 $a$ 个加入的区间移动到第 $b$ 个。 操作数 $1\le n\le 10^5$，保证其他任何数字都是整数且不超过 $10^9$。

题目描述

In this problem at each moment you have a set of intervals. You can move from interval $ (a,b) $ from our set to interval $ (c,d) $ from our set if and only if $ c < a < d $ or $ c < b < d $ . Also there is a path from interval $ I_{1} $ from our set to interval $ I_{2} $ from our set if there is a sequence of successive moves starting from $ I_{1} $ so that we can reach $ I_{2} $ . Your program should handle the queries of the following two types: 1. "1 x y" $ (x&lt;y) $ — add the new interval $ (x,y) $ to the set of intervals. The length of the new interval is guaranteed to be strictly greater than all the previous intervals. 2. "2 a b" $ (a≠b) $ — answer the question: is there a path from $ a $ -th (one-based) added interval to $ b $ -th (one-based) added interval? Answer all the queries. Note, that initially you have an empty set of intervals.

输入输出格式

输入格式

The first line of the input contains integer $ n $ denoting the number of queries, $ (1 \leq n \leq 10^{5}) $ . Each of the following lines contains a query as described above. All numbers in the input are integers and don't exceed $ 10^{9} $ by their absolute value. It's guaranteed that all queries are correct.

输出格式

For each query of the second type print "YES" or "NO" on a separate line depending on the answer.

输入输出样例

输入样例 #1

5
1 1 5
1 5 11
2 1 2
1 2 9
2 1 2

输出样例 #1

NO
YES