Score : $550$ points

问题陈述

给定 $N$ 个编号为 $1$ 到 $N$ 的区间。区间 $i$ 是 $[L_i, R_i]$。

如果两个区间 $[l_a, r_a]$ 和 $[l_b, r_b]$ 满足以下条件之一，则它们被认为相交：$(l_a < l_b < r_a < r_b)$ 或 $(l_b < l_a < r_b < r_a)$。

定义 $f(l, r)$ 为与区间 $[l, r]$ 相交的区间 $i$ 的数量（$1 \leq i \leq N$）。

在所有满足 $0 \leq l < r \leq 10^{9}$ 的整数对 $(l, r)$ 中，找到使 $f(l, r)$ 最大化的对 $(l, r)$。如果有多个这样的对，选择 $l$ 最小的对。如果还有多个对，选择它们中 $r$ 最小的对。（由于 $0 \leq l < r$，要回答的对 $(l, r)$ 是唯一确定的。）

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given $N$ intervals numbered $1$ to $N$. Interval $i$ is $[L_i, R_i]$.

Two intervals $[l_a, r_a]$ and $[l_b, r_b]$ are said to intersect if and only if they satisfy either $(l_a < l_b < r_a < r_b)$ or $(l_b < l_a < r_b < r_a)$.

Define $f(l, r)$ as the number of intervals $i$ ($1 \leq i \leq N$) that intersect with the interval $[l, r]$.

Among all pairs of integers $(l, r)$ satisfying $0 \leq l < r \leq 10^{9}$, find the pair $(l, r)$ that maximizes $f(l, r)$. If there are multiple such pairs, choose the one with the smallest $l$. If there are still multiple pairs, choose the one with the smallest $r$ among them. (Since $0 \leq l < r$, the pair $(l, r)$ to be answered is uniquely determined.)

Constraints

• $1 \leq N \leq 10^{5}$
• $0 \leq L_i < R_i \leq 10^{9}$ $(1 \leq i \leq N)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$L_1$ $R_1$

$L_2$ $R_2$

$\vdots$

$L_N$ $R_N$

Output

Print the sought pair $(l, r)$ in the following format:

$l$ $r$

Sample Input 1

5
1 7
3 9
7 18
10 14
15 20

Sample Output 1

4 11

The maximum value of $f(l, r)$ is $4$, and among the pairs $(l, r)$ that achieve $f(l, r) = 4$, the smallest $l$ is $4$. The pairs $(l, r)$ that satisfy $f(l, r) = 4$ and $l = 4$ are the following five:

• $(l, r) = (4, 11)$
• $(l, r) = (4, 12)$
• $(l, r) = (4, 13)$
• $(l, r) = (4, 16)$
• $(l, r) = (4, 17)$

Among these, the smallest $r$ is $11$, so print $4$ and $11$.

Sample Input 2

11
856977192 996441446
298251737 935869360
396653206 658841528
710569907 929136831
325371222 425309117
379628374 697340458
835681913 939343451
140179224 887672320
375607390 611397526
93530028 581033295
249611310 775998537

Sample Output 2

396653207 887672321