{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eAs a world-famous traveler, Prof. Pang\u0027s research interest is to travel as many places as possible in his life.\u003c/p\u003e\u003cp\u003eWe have a segment $$$[0, n]$$$. There are two travelers on it. The first one is on position $$$p_1$$$ with velocity $$$v_1$$$ (which means s/he can walk $$$v_1$$$ unit on the segment per second). The second one is on position $$$p_2$$$ with velocity $$$v_2$$$.\u003c/p\u003e\u003cp\u003eFrom their respective beginning points, travelers can walk on the segment. They cannot walk outside the segment. Whenever they want to change their direction, they can turn around immediately.\u003c/p\u003e\u003cp\u003ePlease help Prof. Pang to calculate the minimum possible time by which every position of the segment is passed by at least one traveler.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains one integer $$$test~(1\\le test\\le 10000)$$$ – the number of test cases.\u003c/p\u003e\u003cp\u003eThe $$$i$$$-th of the next $$$test$$$ lines contains five numbers $$$n, p_{1, i}, v_{1, i}, p_{2, i}, v_{2, i}$$$ ($$$0 \u0026lt; n \\le 10000$$$, $$$0\\le p_{1, i},p_{2, i} \\le n$$$, $$$0.001 \\le v_{1, i},v_{2, i} \\le 1000$$$). All numbers have at most $$$3$$$ digits after the decimal point.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eFor each test case, we should output one number – the minimum time that every position of the segment is passed by at least one traveler.\u003c/p\u003e\u003cp\u003eYour answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.\u003c/p\u003e"}},{"title":"Examples","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\n10000.0 1.0 0.001 9999.0 0.001\n4306.063 4079.874 0.607 1033.423 0.847\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5001000.0000000000\n3827.8370013755\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}