C. Rectangles

Codeforces

IDCF1028C

Time2000ms

Memory256MB

Difficulty—

geometryimplementationsortings

English · Original

Chinese · Translation

Formal · Original

You are given $n$ rectangles on a plane with coordinates of their bottom left and upper right points. Some $(n-1)$ of the given $n$ rectangles have some common point. A point belongs to a rectangle if this point is strictly inside the rectangle or belongs to its boundary. Find any point with integer coordinates that belongs to at least $(n-1)$ given rectangles. ## Input The first line contains a single integer $n$ ($2 \le n \le 132\,674$) — the number of given rectangles. Each the next $n$ lines contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($-10^9 \le x_1 < x_2 \le 10^9$, $-10^9 \le y_1 < y_2 \le 10^9$) — the coordinates of the bottom left and upper right corners of a rectangle. ## Output Print two integers $x$ and $y$ — the coordinates of any point that belongs to at least $(n-1)$ given rectangles. [samples] ## Note The picture below shows the rectangles in the first and second samples. The possible answers are highlighted. <center>![image](https://espresso.codeforces.com/e47a869e382d2295eeb08173b4b637ceb9c1520d.png)</center>The picture below shows the rectangles in the third and fourth samples. <center>![image](https://espresso.codeforces.com/bff8ead23110ce820ca90a087d0cf0031aa73067.png)</center>

给定平面上的 $n$ 个矩形，每个矩形由其左下角和右上角的坐标给出。在给定的 $n$ 个矩形中，有 $(n -1)$ 个矩形存在一个公共点。一个点属于某个矩形，当且仅当该点严格位于矩形内部或位于其边界上。请找出任意一个具有整数坐标的点，使得该点至少属于给定的 $(n -1)$ 个矩形。第一行包含一个整数 $n$ ($2 lt.eq n lt.eq 132 thin 674$) —— 矩形的数量。接下来的 $n$ 行，每行包含四个整数 $x_1$, $y_1$, $x_2$ 和 $y_2$ ($-10^9 lt.eq x_1 < x_2 lt.eq 10^9$, $-10^9 lt.eq y_1 < y_2 lt.eq 10^9$) —— 分别表示一个矩形的左下角和右上角的坐标。请输出两个整数 $x$ 和 $y$ —— 任意一个至少属于 $(n -1)$ 个给定矩形的点的坐标。下图展示了第一和第二个样例中的矩形，可能的答案已高亮显示。下图展示了第三和第四个样例中的矩形。 ## Input 第一行包含一个整数 $n$ ($2 lt.eq n lt.eq 132 thin 674$) —— 矩形的数量。接下来的 $n$ 行，每行包含四个整数 $x_1$, $y_1$, $x_2$ 和 $y_2$ ($-10^9 lt.eq x_1 < x_2 lt.eq 10^9$, $-10^9 lt.eq y_1 < y_2 lt.eq 10^9$) —— 分别表示一个矩形的左下角和右上角的坐标。 ## Output 请输出两个整数 $x$ 和 $y$ —— 任意一个至少属于 $(n -1)$ 个给定矩形的点的坐标。 [samples] ## Note 下图展示了第一和第二个样例中的矩形，可能的答案已高亮显示。下图展示了第三和第四个样例中的矩形。

**Definitions** Let $ n \in \mathbb{Z} $ with $ 2 \leq n \leq 132674 $. Let $ R_i = [x_{i,1}, x_{i,2}] \times [y_{i,1}, y_{i,2}] \subseteq \mathbb{R}^2 $ for $ i \in \{1, \dots, n\} $ be the given axis-aligned rectangles, where $ x_{i,1} < x_{i,2} $, $ y_{i,1} < y_{i,2} $, and all coordinates are integers. **Given** There exists a point $ p \in \mathbb{R}^2 $ such that $ p $ lies in at least $ n-1 $ of the rectangles $ R_1, \dots, R_n $. **Objective** Find any point $ (x, y) \in \mathbb{Z}^2 $ such that $ (x, y) \in R_i $ for at least $ n-1 $ indices $ i \in \{1, \dots, n\} $. **Constraints** - $ -10^9 \leq x_{i,1} < x_{i,2} \leq 10^9 $ - $ -10^9 \leq y_{i,1} < y_{i,2} \leq 10^9 $ - All rectangle boundaries are inclusive (i.e., point belongs to rectangle if on boundary). - The input guarantees that at least one such integer point exists.

Samples

Input #1

Output #1

1 1

Input #2

Output #2

1 1

Input #3

Output #3

1 1

Input #4

Output #4

3 4

API Response (JSON)

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