{"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\u003eYou are given a sequence of n integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e. \u003c/p\u003e\u003cp\u003eDetermine a real number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e such that the \u003cspan class\u003d\"tex-font-style-it\"\u003eweakness\u003c/span\u003e of the sequence \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e - \u003ci\u003ex\u003c/i\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e - \u003ci\u003ex\u003c/i\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e - \u003ci\u003ex\u003c/i\u003e\u003c/span\u003e is as small as possible.\u003c/p\u003e\u003cp\u003eThe \u003cspan class\u003d\"tex-font-style-it\"\u003eweakness\u003c/span\u003e of a sequence is defined as the maximum value of the \u003cspan class\u003d\"tex-font-style-it\"\u003epoorness\u003c/span\u003e over all segments (contiguous subsequences) of a sequence.\u003c/p\u003e\u003cp\u003eThe \u003cspan class\u003d\"tex-font-style-it\"\u003epoorness\u003c/span\u003e of a segment is defined as the absolute value of sum of the elements of segment.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains one integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 200 000\u003c/span\u003e), the length of a sequence.\u003c/p\u003e\u003cp\u003eThe second line contains \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e|\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e| ≤ 10 000\u003c/span\u003e).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput a real number denoting the minimum possible \u003cspan class\u003d\"tex-font-style-it\"\u003eweakness\u003c/span\u003e of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e1\u003c/sub\u003e - \u003ci\u003ex\u003c/i\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e - \u003ci\u003ex\u003c/i\u003e, ..., \u003ci\u003ea\u003c/i\u003e\u003csub class\u003d\"lower-index\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e - \u003ci\u003ex\u003c/i\u003e\u003c/span\u003e. Your answer will be considered correct if its relative or absolute error doesn\u0027t exceed \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e - 6\u003c/sup\u003e\u003c/span\u003e.\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\u003e3\n1 2 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1.000000000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e4\n1 2 3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2.000000000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","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\u003e10\n1 10 2 9 3 8 4 7 5 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4.500000000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eFor the first case, the optimal value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e is \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e so the sequence becomes \u003cspan class\u003d\"tex-span\"\u003e - 1\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e0\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e and the max poorness occurs at the segment \"-1\" or segment \"1\". The poorness value (answer) equals to \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e in this case. \u003c/p\u003e\u003cp\u003eFor the second sample the optimal value of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e is \u003cspan class\u003d\"tex-span\"\u003e2.5\u003c/span\u003e so the sequence becomes \u003cspan class\u003d\"tex-span\"\u003e - 1.5, - 0.5, 0.5, 1.5\u003c/span\u003e and the max poorness occurs on segment \"-1.5 -0.5\" or \"0.5 1.5\". The poorness value (answer) equals to \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e in this case.\u003c/p\u003e"}}]}