{"trustable":true,"prependHtml":"\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"Freddy Frog is sitting on a stone in the middle of a lake. Suddenly he notices \nFiona Frog who is sitting on another stone. He plans to visit her, but since the \nwater is dirty and full of tourists\u0027 sunscreen, he wants to avoid swimming and \ninstead reach her by jumping. \u003cbr\u003e\n\u003cbr\u003e\nUnfortunately Fiona\u0027s stone is out of his jump range. Therefore Freddy considers \nto use other stones as intermediate stops and reach her by a sequence of several \nsmall jumps. \u003cbr\u003e\n\u003cbr\u003e\nTo execute a given sequence of jumps, a frog\u0027s jump range obviously must be at \nleast as long as the longest jump occuring in the sequence. \u003cbr\u003e\nThe frog distance (humans also call it minimax distance) between two stones therefore \nis defined as the minimum necessary jump range over all possible paths between \nthe two stones. \n\u003cp\u003eYou are given the coordinates of Freddy\u0027s stone, Fiona\u0027s stone and all other \n stones in the lake. Your job is to compute the frog distance between Freddy\u0027s \n and Fiona\u0027s stone. \u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eInput\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n The input will contain one or more test cases. The first line of each test case \n will contain the number of stones n (2 \u0026lt;\u003d n \u0026lt;\u003d 200). The next n lines \n each contain two integers xi, yi (0 \u0026lt;\u003d xi, yi \u0026lt;\u003d 1000) representing the \n coordinates of stone #i. Stone #1 is Freddy\u0027s stone, stone #2 is Fiona\u0027s stone, \n the other n-2 stones are unoccupied. There\u0027s a blank line following each test \n case. Input is terminated by a value of zero (0) for n. \u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eOutput\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n For each test case, print a line saying \"Scenario #x\" and a line saying \n \"Frog Distance \u003d y\" where x is replaced by the test case number (they \n are numbered from 1) and y is replaced by the appropriate real number, printed \n to three decimals. Put a blank line after each test case, even after the last \n one. \u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eSample Input\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n 2\u003cbr\u003e\n 0 0\u003cbr\u003e\n 3 4\u003c/p\u003e\n\u003cp\u003e3\u003cbr\u003e\n 17 4\u003cbr\u003e\n 19 4\u003cbr\u003e\n 18 5\u003c/p\u003e\n\u003cp\u003e0\u003c/p\u003e\n\u003cp\u003e\u003cbr\u003e\n \u003cb\u003eSample Output\u003c/b\u003e\u003cbr\u003e\n \u003cbr\u003e\n Scenario #1\u003cbr\u003e\n Frog Distance \u003d 5.000\u003c/p\u003e\n\u003cp\u003eScenario #2\u003cbr\u003e\n Frog Distance \u003d 1.414\u003c/p\u003e\n"}}]}