Segment Tree

题意翻译

给你 $n\ (1\leq n \leq 5\times 10^5)$ 条线段 $[l_1,r_1],[l_2,r_2],\cdots,[l_n,r_n]\ (1\leq l_i<r_i\leq 2n)$。保证每条线段端点为整数，且 $\forall i,j$，不存在 $l_i=l_j$ 且 $r_i=r_j$，不存在 $r_i=l_j$。 现在用这 $n$ 个点构建一张图，结点 $u,v$ 有边相连当且仅当 $[l_u,r_u]$ 和 $[l_v,r_v]$ 相交，但其中任意一个均不包含另一个。 你的任务是判断这个图是否是一棵树。

题目描述

As the name of the task implies, you are asked to do some work with segments and trees. Recall that a tree is a connected undirected graph such that there is exactly one simple path between every pair of its vertices. You are given $ n $ segments $ [l_1, r_1], [l_2, r_2], \dots, [l_n, r_n] $ , $ l_i < r_i $ for every $ i $ . It is guaranteed that all segments' endpoints are integers, and all endpoints are unique — there is no pair of segments such that they start in the same point, end in the same point or one starts in the same point the other one ends. Let's generate a graph with $ n $ vertices from these segments. Vertices $ v $ and $ u $ are connected by an edge if and only if segments $ [l_v, r_v] $ and $ [l_u, r_u] $ intersect and neither of it lies fully inside the other one. For example, pairs $ ([1, 3], [2, 4]) $ and $ ([5, 10], [3, 7]) $ will induce the edges but pairs $ ([1, 2], [3, 4]) $ and $ ([5, 7], [3, 10]) $ will not. Determine if the resulting graph is a tree or not.

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 1 \le n \le 5 \cdot 10^5 $ ) — the number of segments. The $ i $ -th of the next $ n $ lines contain the description of the $ i $ -th segment — two integers $ l_i $ and $ r_i $ ( $ 1 \le l_i < r_i \le 2n $ ). It is guaranteed that all segments borders are pairwise distinct.

输出格式

Print "YES" if the resulting graph is a tree and "NO" otherwise.

输入输出样例

输入样例 #1

6
9 12
2 11
1 3
6 10
5 7
4 8

输出样例 #1

YES

输入样例 #2

5
1 3
2 4
5 9
6 8
7 10

输出样例 #2

NO

输入样例 #3

5
5 8
3 6
2 9
7 10
1 4

输出样例 #3

NO

说明

The graph corresponding to the first example:  The graph corresponding to the second example:  The graph corresponding to the third example: