A9167 | Ping-Pong

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" $(x<y)$ — 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.

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.

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