{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"Freddy Frog is sitting on a stone in the middle of a lake. Suddenly he notices Fiona Frog who is sitting on another stone. He plans to visit her, but since the water is dirty and full of tourists\u0027 sunscreen, he wants to avoid swimming and instead reach her by jumping. \r\u003cbr\u003eUnfortunately Fiona\u0027s stone is out of his jump range. Therefore Freddy considers to use other stones as intermediate stops and reach her by a sequence of several small jumps. \r\u003cbr\u003eTo execute a given sequence of jumps, a frog\u0027s jump range obviously must be at least as long as the longest jump occuring in the sequence. \r\u003cbr\u003eThe frog distance (humans also call it minimax distance) between two stones therefore is defined as the minimum necessary jump range over all possible paths between the two stones. \r\u003cbr\u003e\r\u003cbr\u003eYou are given the coordinates of Freddy\u0027s stone, Fiona\u0027s stone and all other stones in the lake. Your job is to compute the frog distance between Freddy\u0027s and Fiona\u0027s stone.\r\u003cbr\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The input will contain one or more test cases. The first line of each test case will contain the number of stones n (2\u0026lt;\u003dn\u0026lt;\u003d200). The next n lines each contain two integers xi,yi (0 \u0026lt;\u003d xi,yi \u0026lt;\u003d 1000) representing the coordinates of stone #i. Stone #1 is Freddy\u0027s stone, stone #2 is Fiona\u0027s stone, the other n-2 stones are unoccupied. There\u0027s a blank line following each test case. Input is terminated by a value of zero (0) for n. "}},{"title":"Output","value":{"format":"HTML","content":"For each test case, print a line saying \"Scenario #x\" and a line saying \"Frog Distance \u003d y\" where x is replaced by the test case number (they are numbered from 1) and y is replaced by the appropriate real number, printed to three decimals. Put a blank line after each test case, even after the last one. "}},{"title":"Sample","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\r\n0 0\r\n3 4\r\n\r\n3\r\n17 4\r\n19 4\r\n18 5\r\n\r\n0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eScenario #1\r\nFrog Distance \u003d 5.000\r\n\r\nScenario #2\r\nFrog Distance \u003d 1.414\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}