A13583 | Bicolored Segments

You are given $n$ segments $[l_1, r_1], [l_2, r_2], \dots, [l_n, r_n]$ . Each segment has one of two colors: the $i$ -th segment's color is $t_i$ .

Let's call a pair of segments $i$ and $j$ bad if the following two conditions are met:

- $t_i \ne t_j$ ;
- the segments $[l_i, r_i]$ and $[l_j, r_j]$ intersect, embed or touch, i. e. there exists an integer $x$ such that $x \in [l_i, r_i]$ and $x \in [l_j, r_j]$ .

Calculate the maximum number of segments that can be selected from the given ones, so that there is no bad pair among the selected ones.

The first line contains a single integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — number of segments.

The next $n$ lines contains three integers $l_i, r_i, t_i$ ( $1 \le l_i \le r_i \le 10^9; t_i \in \{1, 2\}$ ) — description of the $i$ -th segment.

Print the maximum number of segments that can be selected, so that there is no bad pair among the selected segments.