시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 512 MB92553664250037.532%

문제

집과 사무실을 통근하는 n명의 사람들이 있다. 각 사람의 집과 사무실은 수평선 상에 있는 서로 다른 점에 위치하고 있다. 임의의 두 사람 A, B에 대하여, A의 집 혹은 사무실의 위치가 B의 집 혹은 사무실의 위치와 같을 수 있다. 통근을 하는 사람들의 편의를 위하여 일직선 상의 어떤 두 점을 잇는 철로를 건설하여, 기차를 운행하려고 한다. 제한된 예산 때문에, 철로의 길이는 d로 정해져 있다. 집과 사무실의 위치 모두 철로 선분에 포함되는 사람들의 수가 최대가 되도록, 철로 선분을 정하고자 한다.

양의 정수 d와 n 개의 정수쌍, (hi, oi), 1 ≤ i ≤ n,이 주어져 있다. 여기서 hi와 oi는 사람 i의 집과 사무실의 위치이다. 길이 d의 모든 선분 L에 대하여, 집과 사무실의 위치가 모두 L에 포함되는 사람들의 최대 수를 구하는 프로그램을 작성하시오.

그림 1. 8 명의 집과 사무실의 위치

그림 1 에 있는 예를 고려해보자. 여기서 n = 8, (h1, o1) = (5, 40), (h2, o2) = (35, 25), (h3, o3) = (10, 20), (h4, o4) = (10, 25), (h5, o5) = (30, 50), (h6, o6) = (50, 60), (h7, o7) = (30, 25), (h8, o8) = (80, 100)이고, d = 30이다. 이 예에서, 위치 10 과 40 사이의 빨간색 선분 L이, 가장 많은 사람들에 대하여 집과 사무실 위치 모두 포함되는 선분 중 하나이다. 따라서 답은 4 이다.

입력

입력은 표준입력을 사용한다. 첫 번째 줄에 사람 수를 나타내는 양의 정수 n (1 ≤ n ≤ 100,000)이 주어진다. 다음 n개의 각 줄에 정수 쌍 (hi, oi)가 주어진다. 여기서 hi와 oi는 −100,000,000이상, 100,000,000이하의 서로 다른 정수이다. 마지막 줄에, 철로의 길이를 나타내는 정수 d (1 ≤ d ≤ 200,000,000)가 주어진다.

출력

출력은 표준출력을 사용한다. 길이 d의 임의의 선분에 대하여, 집과 사무실 위치가 모두 그 선분에 포함되는 사람들의 최대 수를 한 줄에 출력한다. 

예제 입력 1

8
5 40
35 25
10 20
10 25
30 50
50 60
30 25
80 100
30

예제 출력 1

4

예제 입력 2

4
20 80
70 30
35 65
40 60
10

예제 출력 2

0

예제 입력 3

5
-5 5
30 40
-5 5
50 40
5 -5
10

예제 출력 3

3
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For any two persons A and B, home or office of A can be located at the same point as home or office of B. For the convenience of the persons who commute, we are going to build a railway as a line segment between two points on the horizontal line and operate a rail transport with the stations at points of all homes or offices on the railway. Due to the limited budget, the length of the railway is fixed as d. We want to locate a line segment (railway) L of length d so that the number of persons whose both home and office locations are contained in L is maximized.<\/p>\r\n\r\n<p>Given a positive integer d and n pairs of integers, (h<sub>i<\/sub>, o<sub>i<\/sub>), 1 &le; i &le; n, where h<sub>i<\/sub> and o<sub>i<\/sub> are the home location and the office location of person i, respectively, you write a program which prints the maximum number of persons whose both home and office locations are contained in L over all line segments L of length d.<\/p>\r\n\r\n<p style=\"text-align:center\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/13334\/1.png\" style=\"height:140px; text-align:center; width:422px\" \/><\/p>\r\n\r\n<p style=\"text-align:center\">Figure 1. Eight pairs of home and office locations.<\/p>\r\n\r\n<p>Consider an example shown in Figure l where n = 8, (h<sub>1<\/sub>, o<sub>1<\/sub>) = (5, 40), (h<sub>2<\/sub>, o<sub>2<\/sub>) = (35, 25), (h<sub>3<\/sub>, o<sub>3<\/sub>) = (10, 20), (h<sub>4<\/sub>, o<sub>4<\/sub>) = (10, 25), (h<sub>5<\/sub>, o<sub>5<\/sub>) = (30, 50), (h<sub>6<\/sub>, o<sub>6<\/sub>) = (50, 60), (h<sub>7<\/sub>, o<sub>7<\/sub>) = (30, 25), (h<sub>8<\/sub>, o<sub>8<\/sub>) = (80, 100), and d = 30. In this example, the line segment L with red color between 10 and 40 is one of the railway segments which can be located so that the number of persons whose both home and office locations are contained is maximum, thus the answer is 4.<\/p>\r\n","input":"<p>Your program is to read from standard input. The first line contains an integer n (1 &le; n &le; 100,000) where n is the number of persons. In each of the following n lines, a pair of integers, (h<sub>i<\/sub>, o<sub>i<\/sub>) are given where h<sub>i<\/sub> and o<sub>i<\/sub> are distinct integers between &minus;100,000,000 and 100,000,000, inclusively. The last line has an integer d (1 &le; d &le; 200,000,000) that represents the length of the railway segment.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for the input. The line should contain an integer representing the maximum number of persons whose both home and office locations are contained in L over all line segments L of length d.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]