Preparando MOJI
Filled with optimism, Hyunuk will host a conference about how great this new year will be!
The conference will have $$$n$$$ lectures. Hyunuk has two candidate venues $$$a$$$ and $$$b$$$. For each of the $$$n$$$ lectures, the speaker specified two time intervals $$$[sa_i, ea_i]$$$ ($$$sa_i \le ea_i$$$) and $$$[sb_i, eb_i]$$$ ($$$sb_i \le eb_i$$$). If the conference is situated in venue $$$a$$$, the lecture will be held from $$$sa_i$$$ to $$$ea_i$$$, and if the conference is situated in venue $$$b$$$, the lecture will be held from $$$sb_i$$$ to $$$eb_i$$$. Hyunuk will choose one of these venues and all lectures will be held at that venue.
Two lectures are said to overlap if they share any point in time in common. Formally, a lecture held in interval $$$[x, y]$$$ overlaps with a lecture held in interval $$$[u, v]$$$ if and only if $$$\max(x, u) \le \min(y, v)$$$.
We say that a participant can attend a subset $$$s$$$ of the lectures if the lectures in $$$s$$$ do not pairwise overlap (i.e. no two lectures overlap). Note that the possibility of attending may depend on whether Hyunuk selected venue $$$a$$$ or venue $$$b$$$ to hold the conference.
A subset of lectures $$$s$$$ is said to be venue-sensitive if, for one of the venues, the participant can attend $$$s$$$, but for the other venue, the participant cannot attend $$$s$$$.
A venue-sensitive set is problematic for a participant who is interested in attending the lectures in $$$s$$$ because the participant cannot be sure whether the lecture times will overlap. Hyunuk will be happy if and only if there are no venue-sensitive sets. Determine whether Hyunuk will be happy.
The first line contains an integer $$$n$$$ ($$$1 \le n \le 100\,000$$$), the number of lectures held in the conference.
Each of the next $$$n$$$ lines contains four integers $$$sa_i$$$, $$$ea_i$$$, $$$sb_i$$$, $$$eb_i$$$ ($$$1 \le sa_i, ea_i, sb_i, eb_i \le 10^9$$$, $$$sa_i \le ea_i, sb_i \le eb_i$$$).
Print "YES" if Hyunuk will be happy. Print "NO" otherwise.
You can print each letter in any case (upper or lower).
2 1 2 3 6 3 4 7 8
YES
3 1 3 2 4 4 5 6 7 3 4 5 5
NO
6 1 5 2 9 2 4 5 8 3 6 7 11 7 10 12 16 8 11 13 17 9 12 14 18
YES
In second example, lecture set $$$\{1, 3\}$$$ is venue-sensitive. Because participant can't attend this lectures in venue $$$a$$$, but can attend in venue $$$b$$$.
In first and third example, venue-sensitive set does not exist.
Informação
Provedor Codeforces
Código CF1284D
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Datas 09/05/2023 09:57:54
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