On the circle, $$$2n$$$ points are marked, arranged at equal intervals in a clockwise direction. These points have been randomly (more on this in the Input section) connected in $$$n$$$ pairs to form $$$n$$$ chords. Your task is to find the largest possible set of chords in which no two intersect, and output the size of this set.
The first line of the standard input contains a single integer $$$n$$$ ($$$1 \leq n \leq 100\,000$$$), indicating the number of chords.
In the next $$$n$$$ lines, there are two integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \leq a_i \lt b_i \leq 2n$$$) each, indicating that the chord connects the $$$a_i$$$-th and $$$b_i$$$-th points. All $$$2n$$$ values of $$$a_i$$$ and $$$b_i$$$ are pairwise distinct.
NOTE: Out of laziness of the jury To make the task more interesting, all tests for this task (except for the sample test) were randomly generated. For each test, a value of $$$n$$$ and a seed for the random number generator were chosen. Then a random permutation of numbers from $$$1$$$ to $$$2n$$$ was generated, which was divided into $$$n$$$ pairs. Then, in each pair, the numbers could be swapped to ensure the condition $$$a_i \lt b_i$$$.
The sample test was created manually, but in order for the solution to be accepted, it must also be solved correctly.
The output should contain a single integer, indicating the size of the largest set of non-intersecting chords.
5 1 2 4 10 7 9 3 5 6 8
3
The chords in the sample test look as follows:
One of the possible largest correct sets of chords contains the chords connecting points $$$1$$$ and $$$2$$$, $$$3$$$ and $$$5$$$, and $$$6$$$ and $$$8$$$.
