Задача 39377. Particle Mu

Having delved into the study of physics in quarantine, the cows discovered "mu-particles"
They are currently experimenting with N "mu-particles" (1 ≤N ≤ 10⁵). Particle i has a "spin" described by two integers x_i and y_i in the range −10⁹…10 ⁹ inclusive. Sometimes two "mu-particles" interact. This can only happen to particles with spins (x_i,y_i) and (x_j,y_j) that have x_i≤x_j and y_i≤y_j. Under these conditions, exactly one of these particles disappears (and nothing happens to the other). At most one interaction can happen at any given time.

The cows want to know the minimum number of "mu-particles" that can remain after some arbitrary sequence of interactions.

Input
The first line contains one integer N, the initial number of "mu-particles". Each of the following N lines contains two space-separated integers defining the spin of this particle. All spins are different.
Imprint
One integer, the minimum number of "mu-particles" that can remain after some arbitrary sequence of interactions.

Examples

#	Input	Output	Note
1	4 10 0 1 -1 0 0 -1	1	One of the possible interaction sequences: Particles 1 and 4 interact, particle 1 disappears. Particles 2 and 4 interact, particle 4 disappears. Particles 2 and 3 interact, particle 3 disappears. Only particle 2 remains.
2	3 0 0 1 1 -1 3	2	Particle 3 cannot interact with any of the other particles, so it must remain. One of particles 1 and 2 should also remain.