Intervals and Queries 2

Given $N$ queries, process them in order. There are two types of queries, as follows. At the start, the set is empty.

• 1 x y (x < y): Adds a new interval $(x, y)$ to the set. The new interval is larger than every interval added before it.
• 2 a b ($a \neq b$): Prints 1 if there is a path from the $a$-th added interval to the $b$-th added interval, and 0 otherwise. The first interval added is the 1st interval.

To move from interval $(x_1, y_1)$ to interval $(x_2, y_2)$, it must hold that $x_2 < x_1 < y_2$ or $x_2 < y_1 < y_2$. A path from interval $I_1$ to interval $I_2$ exists when you can move from $I_1$ to $I_2$ using only the intervals in the set.

The first line contains the number of queries $N$ ($1 \le N \le 100{,}000$). Each of the next $N$ lines contains one query. All values in the input are integers whose absolute value is at most $10^9$. A type 2 query is given only after at least two intervals have been added to the set.

For each type 2 query, print the result.