Problem Statement

For a set $S$ of pairs of non-negative integers, and a non-negative integer $x$, let $f_S(x)$ defined as $\displaystyle f_S(x)=\min_{(a, b) \in S} \left| \left| x-a \right| - b \right|$.

We have a set $T$ of pairs of non-negative integers. Initially, $T=\lbrace (A, B)\rbrace$.

Process $Q$ queries. The $i$-th query gives you three non-negative integers $t_i$, $a_i$, and $b_i$, and asks you to do the following.

• If $t_i=1$, add to $T$ the pair $(a_i, b_i)$ of non-negative integers.
• If $t_i=2$, print the minimum value of $f_{T}(x)$ for a non-negative integer $x$ such that $a_i \leq x \leq b_i$.

Constraints

• $1 \leq Q \leq 2 \times 10^5$
• $0 \leq A,B \leq 10^{9}$
• $t_i$ is $1$ or $2$.
• $0 \leq a_i,b_i \leq 10^{9}$
• If $t_i=2$, then $a_i \leq b_i$.
• There is at least one query with $t_i=2$.
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

Q A B
t_1 a_1 b_1
t_2 a_2 b_2
\vdots
t_Q a_Q b_Q

Output

For each query with $t_i=2$ in the given order, print the answer in its own line.