Segment Set Queries

You are given an initially empty set of segments. You need to process \(q\) queries. Each query is of one of the following three types:

1. Add a new segment \([l_i, r_i]\).
2. For every segment in the set that intersects with \([l_i, r_i]\), modify it to be its intersection with \([l_i, r_i]\).
3. Output the sum of lengths of the intersections between each segment in the set and \([l_i, r_i]\).

Two segments \([a,b]\) and \([c,d]\) intersect if and only if \(\max\{a,c\} \leq \min\{b,d\}\). Their intersection is \([\max\{a,c\}, \min\{b,d\}]\). The length of a segment \([a,b]\) is defined as \(b-a\). Note that a segment may degenerate to a point.

Some test cases require performing these operations online.

inputFormat

The first line contains an integer \(q\) \( (1 \le q \le 10^5)\), the number of queries. Each of the next \(q\) lines contains three integers:

op l r

Here, op is an integer (1, 2, or 3) denoting the type of the query, and \(l\), \(r\) represent the left and right endpoints of the segment \([l, r]\). It is guaranteed that \(l \le r\).

outputFormat

For each query of type 3, output one line containing a single integer – the sum of the lengths of intersection between \([l, r]\) and each segment in the set.

sample

6
1 1 5
1 3 7
3 2 6
2 4 4
3 1 10
1 2 8

6
0