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1 초 256 MB0000.000%

문제

루카(Luka)는 그의 강아지를 위해 금 목줄을 사고 공원을 나갔습니다. 루카는 공원에 들어서자 그의 강아지를 놓아주었고 루카는 자신이 가장 빠르게 갈 수 있는 출구로 갔습니다. 근데 그의 강아지는 T초 이후에 루카를 따라잡는다고 합니다. 근데 루카는 강아지가 목줄을 잃어버린 것을 보고 기분이 안 좋아졌습니다. 그래서 그는 어느 부분이 강아지의 목줄을 잃어버릴 수 있게 만들 수 있는지 알아보기로 했습니다.

공원은 2차원 평면이고, 루카와 강아지는 점으로 표현합니다. 루카가 강아지를 놓아 주었을 때, 둘 다 (Ax, Ay)의 좌표에 위치해 있었습니다. 루카와 강아지는 전후좌우 4방향으로 움직일 수 있고, 속력은 정확히 1m/s 라고 합니다. 그들은 따로 움직이고, 언제나 방향을 틀 수 있습니다. 이 말은 0.37m는 위로, 0.63m는 오른쪽으로 1초동안 갈 수 있다는 것입니다.

정확히 T초 후 루카는 출구에 가장 빠른 길로 왔고, 강아지는 그를 따라잡았습니다. 그때 그들은 같은 좌표 (Bx, By)에 있었습니다. 그리고 공원에는 네모난 정원이 중간중간 있고 그 곳에는 루카와 강아지 모두 못 들어가는 곳이지만 그 가장자리로는 갈 수 있다고 합니다. 정원은 다른 정원과 만나지 않고 직사각형으로 표현됩니다. 

노트 : 강아지는 가끔 멈출 수 있고, 루카는 출구에 도착하기 전까지는 1m/s의 속도로 항상 걸었습니다.

입력

첫째 줄에는 공원에 있는 정원의 개수 N(0 ≤ N ≤ 100)이 주어집니다.

둘째 줄에는 공원의 입구(루카가 강아지를 놓아준 곳)의 좌표 Ax, Ay(0 ≤ Ax, Ay ≤ 10000)가 주어집니다.

셋째 줄에는 공원의 출구(루카와 강아지가 만난 곳)의 좌표 Bx, By(0 ≤ Bx, By ≤ 10000)가 주어지며, Ax, Ay 와 다릅니다.

다음 N줄에서는 정수 4개 X1, Y1, X2, Y2 (0 ≤ X1 < X2 ≤ 10000, 0 ≤ Y1 < Y2 ≤ 10000)가 주어지며,    (X1, Y1)은 정원의 왼쪽 아래 좌표, (X2, Y2)는 오른쪽 위 좌표입니다. 이 정원들은 정원의 입구나 출구를 포함하고 있지 않습니다.

마지막 줄에는 루카가 강아지를 기다린 시간인 T(0 ≤ T ≤ 10000)가 주어집니다.

출력

목줄을 잃어버릴 수 있는 위치를 출력합니다.

0.01의 오차까지는 정답으로 인정합니다.

예제 입력 1

2
1 1
5 5
2 2 3 6
4 3 7 4
0

예제 출력 1

7.000000

예제 입력 2

0
1 1
5 5
2

예제 출력 2

34.000000

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T&nbsp;&le; 10000)\uac00 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\ubaa9\uc904\uc744 \uc783\uc5b4\ubc84\ub9b4 \uc218 \uc788\ub294 \uc704\uce58\ub97c \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>0.01\uc758 \uc624\ucc28\uae4c\uc9c0\ub294 \uc815\ub2f5\uc73c\ub85c \uc778\uc815\ud569\ub2c8\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/64b18b3c-883a-4042-b437-81903977796e\/-\/preview\/\" style=\"width: 211px; height: 180px;\" \/><\/p>\r\n","sample_explain_2":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/aa7d86f8-ef01-4c1c-a027-03ff4a191999\/-\/preview\/\" style=\"width: 161px; height: 159px;\" \/><\/p>\r\n"},{"problem_id":"3094","problem_lang":"1","title":"OGRLICA","description":"<p>Luka had recently bought an expensive gold collar for his dog, and took him for a walk in the park. 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For example, it is possible that one of them moves 0.37 meters up and then continues 0.63 meters to the right while other moves 1 meter to the left during one second.&nbsp;<\/p>\r\n\r\n<p>Exactly T seconds after Luka came through one of the fastest way to the exit, the dog caught up with him and once again they were at the same coordinates (Bx, By). Also in the park, there are rectangularfence enclosed gardens through which neither Luka nor the dog can move. These gardens are represented as rectangles in the plane that do not touch or intersect each other. Luka and the dog are able to move by the edges of the gardens.&nbsp;<\/p>\r\n\r\n<p>Note: it is possible that the dog stood for a while in one place. 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출처

Olympiad > Croatian Highschool Competitions in Informatics > 2011 > Final Exam #2 2번