{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":" Benjamin Forest VIII is a king of a country. One of his best friends Nod lives in a village far from his castle. Nod gets seriously sick and is on the verge of death. Benjamin orders his subordinate Red to bring good medicine for him as soon as possible. However, there is no road from the castle to the village. Therefore, Red needs to climb over mountains and across canyons to reach the village. He has decided to get to the village on the shortest path on a map, that is, he will move on the straight line between the castle and the village. Then his way can be considered as polyline with \u003ci\u003en\u003c/i\u003e points (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e)... (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e) as illustlated in the following figure. \u003cbr\u003e \u003cimg src\u003d\"CDN_BASE_URL/864843266f4c07929879698f305a36f0?v\u003d1715242755\" style\u003d\"height: 15.0em;max-width: 100.0%;max-height: 100.0%;\"\u003e \u003cbr\u003e Here, \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e and \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e are coordinates of point \u003ci\u003ei\u003c/i\u003e. The castle is located on the point (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e), and the village is located on the point (\u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e). Red can walk with speed \u003ci\u003ev\u003c/i\u003e\u003csub\u003e\u003ci\u003ew\u003c/i\u003e\u003c/sub\u003e. Also, since he has a skill to cut a tunnel through a mountain horizontally, he can move strictly inside the mountain with speed \u003ci\u003ev\u003c/i\u003e\u003csub\u003e\u003ci\u003ec\u003c/i\u003e\u003c/sub\u003e. Your job is to write a program to find the minimum time to get to the village. \u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eInput\u003c/b\u003e\u003c/div\u003eThe input is given in the following format: \u003ci\u003en\u003c/i\u003e \u003ci\u003ev\u003c/i\u003e\u003csub\u003e\u003ci\u003ew\u003c/i\u003e\u003c/sub\u003e \u003ci\u003ev\u003c/i\u003e\u003csub\u003e\u003ci\u003ec\u003c/i\u003e\u003c/sub\u003e \u003ci\u003ex\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e \u003ci\u003ey\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e ... \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e You may assume all the following: 1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 1000, 1 ≤ \u003ci\u003ev\u003c/i\u003e\u003csub\u003e\u003ci\u003ew\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ev\u003c/i\u003e\u003csub\u003e\u003ci\u003ec\u003c/i\u003e\u003c/sub\u003e ≤ 10, -10000 ≤ \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e, \u003ci\u003ey\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 10000, and \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e \u0026lt; \u003ci\u003ex\u003c/i\u003e\u003csub\u003e\u003ci\u003ej\u003c/i\u003e\u003c/sub\u003e for all \u003ci\u003ei\u003c/i\u003e \u0026lt; \u003ci\u003ej\u003c/i\u003e. \u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eOutput\u003c/b\u003e\u003c/div\u003eYou should print the minimum time required to get to the village in a line. Each minimum time should be given as a decimal with an arbitrary number of fractional digits and with an absolute error of at most 10\u003csup\u003e-6\u003c/sup\u003e. \u003cbr\u003e"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n2 1\n0 0\n50 50\n100 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e70.710678\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 2","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n1 1\n0 0\n50 50\n100 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e100.000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 3","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n1 2\n0 0\n50 50\n100 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e50.000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 4","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3\n2 1\n0 0\n100 100\n150 50\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e106.066017\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 5","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6\n1 2\n0 0\n50 50\n100 0\n150 0\n200 50\n250 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e150.000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 6","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2\n1 2\n0 0\n100 0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e100.000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}