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 $a_i \leq x \leq b_i$.

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.

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.

Sample Input 1

4 0 5
1 3 11
2 7 8
1 8 2
2 8 9

Sample Output 1

2
1

In the second query, $T=\lbrace(0, 5), (3, 11) \rbrace$. For x=7, we have $f_T(7)=\min \lbrace \left| \left|7-0\right|-5\right|, \left| \left|7-3\right|-11\right| \rbrace=\min \lbrace 2, 7 \rbrace=2. Similarly, f_T(8)=3.$ Thus, the answer is $\min \lbrace 2, 3 \rbrace =2$.
In the fourth query, $T=\lbrace(0, 5), (3, 11), (8, 2) \rbrace. In 8 \leq x \leq 9, f_T(x)$ takes the minimum value f_T(9)=1 at x=9.

Sample Input 2

2 1 2
1 2 3
2 2 6

Sample Output 2

0

Sample Input 3

20 795629912 123625148
2 860243184 892786970
2 645778367 668513124
1 531411849 174630323
1 635062977 195695960
2 382061637 411843651
1 585964296 589553566
1 310118888 68936560
1 525351160 858166280
2 395304415 429823333
2 583145399 703645715
2 97768492 218377432
1 707220749 459967102
1 210842017 363390878
2 489541834 553583525
2 731279777 811513313
1 549864943 493384741
1 815378318 826084592
2 369622093 374205455
1 78240781 821999998
2 241667193 243982581

Sample Output 3

26468090
3491640
25280111
9543684
0
22804896
20649370
19245624
4849993
484865

见题面 Input 部分

见题面 Output 部分