F. Bicolored Segmentstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputPrint the maximum number of segments that can be selected, so that there is no bad pair among the selected segments.ExamplesInput
3
1 3 1
4 6 2
2 5 1
Output
2
Input
5
5 8 1
1 3 2
3 4 2
6 6 1
2 10 2
Output
4
Input
7
19 20 1
13 15 2
6 11 2
4 10 1
14 17 1
13 13 2
5 9 1
Output
5

3
1 3 1
4 6 2
2 5 1

2 
['data structures', 'dp', 'graph matchings', 'sortings', '*2600']