{"trustable":false,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cstyle\u003e\n\u003c!--\n /* Font Definitions */\n @font-face\n\t{font-family:Mangal;\n\tpanose-1:2 4 5 3 5 2 3 3 2 2;}\n@font-face\n\t{font-family:\"Cambria Math\";\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;}\n@font-face\n\t{font-family:Cambria;\n\tpanose-1:2 4 5 3 5 4 6 3 2 4;}\n@font-face\n\t{font-family:Calibri;\n\tpanose-1:2 15 5 2 2 2 4 3 2 4;}\n@font-face\n\t{font-family:Tahoma;\n\tpanose-1:2 11 6 4 3 5 4 4 2 4;}\n@font-face\n\t{font-family:Garamond;\n\tpanose-1:2 2 4 4 3 3 1 1 8 3;}\n@font-face\n\t{font-family:Verdana;\n\tpanose-1:2 11 6 4 3 5 4 4 2 4;}\n@font-face\n\t{font-family:\"Bernard MT Condensed\";\n\tpanose-1:2 5 8 6 6 9 5 2 4 4;}\n@font-face\n\t{font-family:\"Bookman Old Style\";\n\tpanose-1:2 5 6 4 5 5 5 2 2 4;}\n@font-face\n\t{font-family:\"Courier 10 Pitch\";}\n@font-face\n\t{font-family:\"DejaVu Sans\";}\n@font-face\n\t{font-family:\"\\@Courier 10 Pitch\";}\n@font-face\n\t{font-family:\"\\@DejaVu Sans\";}\n /* Style Definitions */\n p.MsoNormal, li.MsoNormal, div.MsoNormal\n\t{margin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:10.0pt;\n\tmargin-left:0in;\n\ttext-align:justify;\n\tline-height:115%;\n\tfont-size:12.0pt;\n\tfont-family:\"Garamond\",\"serif\";}\nh1\n\t{mso-style-link:\"Heading 1 Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tline-height:115%;\n\tpage-break-after:avoid;\n\tfont-size:14.0pt;\n\tfont-family:\"Cambria\",\"serif\";\n\tcolor:green;}\nh2\n\t{mso-style-link:\"Heading 2 Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tpage-break-after:avoid;\n\tfont-size:16.0pt;\n\tfont-family:\"Arial\",\"sans-serif\";\n\tcolor:black;}\nh3\n\t{mso-style-link:\"Heading 3 Char\";\n\tmargin-top:10.0pt;\n\tmargin-right:0in;\n\tmargin-bottom:0in;\n\tmargin-left:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tline-height:115%;\n\tpage-break-after:avoid;\n\tfont-size:12.0pt;\n\tfont-family:\"Garamond\",\"serif\";\n\tcolor:#4F81BD;}\np.MsoHeader, li.MsoHeader, div.MsoHeader\n\t{mso-style-link:\"Header Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tfont-size:12.0pt;\n\tfont-family:\"Garamond\",\"serif\";}\np.MsoFooter, li.MsoFooter, div.MsoFooter\n\t{mso-style-link:\"Footer Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tfont-size:12.0pt;\n\tfont-family:\"Garamond\",\"serif\";}\np.MsoTitle, li.MsoTitle, div.MsoTitle\n\t{mso-style-link:\"Title Char\";\n\tmargin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:12.0pt;\n\tmargin-left:0in;\n\ttext-align:center;\n\tfont-size:36.0pt;\n\tfont-family:\"Bernard MT Condensed\",\"serif\";\n\tcolor:green;\n\tletter-spacing:.25pt;}\np.MsoTitleCxSpFirst, li.MsoTitleCxSpFirst, div.MsoTitleCxSpFirst\n\t{mso-style-link:\"Title Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:center;\n\tfont-size:36.0pt;\n\tfont-family:\"Bernard MT Condensed\",\"serif\";\n\tcolor:green;\n\tletter-spacing:.25pt;}\np.MsoTitleCxSpMiddle, li.MsoTitleCxSpMiddle, div.MsoTitleCxSpMiddle\n\t{mso-style-link:\"Title Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:center;\n\tfont-size:36.0pt;\n\tfont-family:\"Bernard MT Condensed\",\"serif\";\n\tcolor:green;\n\tletter-spacing:.25pt;}\np.MsoTitleCxSpLast, li.MsoTitleCxSpLast, div.MsoTitleCxSpLast\n\t{mso-style-link:\"Title Char\";\n\tmargin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:12.0pt;\n\tmargin-left:0in;\n\ttext-align:center;\n\tfont-size:36.0pt;\n\tfont-family:\"Bernard MT Condensed\",\"serif\";\n\tcolor:green;\n\tletter-spacing:.25pt;}\np.MsoSubtitle, li.MsoSubtitle, div.MsoSubtitle\n\t{mso-style-link:\"Subtitle Char\";\n\tmargin-top:6.0pt;\n\tmargin-right:0in;\n\tmargin-bottom:0in;\n\tmargin-left:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:center;\n\tline-height:115%;\n\tfont-size:24.0pt;\n\tfont-family:\"Bookman Old Style\",\"serif\";\n\tletter-spacing:.75pt;\n\tfont-weight:bold;}\np.MsoBodyText3, li.MsoBodyText3, div.MsoBodyText3\n\t{mso-style-link:\"Body Text 3 Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tfont-size:12.0pt;\n\tfont-family:\"Verdana\",\"sans-serif\";\n\tcolor:black;}\na:link, span.MsoHyperlink\n\t{color:blue;\n\ttext-decoration:underline;}\na:visited, span.MsoHyperlinkFollowed\n\t{color:purple;\n\ttext-decoration:underline;}\npre\n\t{mso-style-link:\"HTML Preformatted Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tfont-size:10.0pt;\n\tfont-family:\"Courier New\";}\np.MsoAcetate, li.MsoAcetate, div.MsoAcetate\n\t{mso-style-link:\"Balloon Text Char\";\n\tmargin:0in;\n\tmargin-bottom:.0001pt;\n\ttext-align:justify;\n\tfont-size:8.0pt;\n\tfont-family:\"Tahoma\",\"sans-serif\";}\np.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing\n\t{margin:0in;\n\tmargin-bottom:.0001pt;\n\tfont-size:12.0pt;\n\tfont-family:\"Garamond\",\"serif\";}\np.MsoListParagraph, li.MsoListParagraph, div.MsoListParagraph\n\t{margin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:10.0pt;\n\tmargin-left:.5in;\n\tline-height:115%;\n\tfont-size:11.0pt;\n\tfont-family:\"Calibri\",\"sans-serif\";}\np.MsoListParagraphCxSpFirst, li.MsoListParagraphCxSpFirst, div.MsoListParagraphCxSpFirst\n\t{margin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:0in;\n\tmargin-left:.5in;\n\tmargin-bottom:.0001pt;\n\tline-height:115%;\n\tfont-size:11.0pt;\n\tfont-family:\"Calibri\",\"sans-serif\";}\np.MsoListParagraphCxSpMiddle, li.MsoListParagraphCxSpMiddle, div.MsoListParagraphCxSpMiddle\n\t{margin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:0in;\n\tmargin-left:.5in;\n\tmargin-bottom:.0001pt;\n\tline-height:115%;\n\tfont-size:11.0pt;\n\tfont-family:\"Calibri\",\"sans-serif\";}\np.MsoListParagraphCxSpLast, li.MsoListParagraphCxSpLast, div.MsoListParagraphCxSpLast\n\t{margin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:10.0pt;\n\tmargin-left:.5in;\n\tline-height:115%;\n\tfont-size:11.0pt;\n\tfont-family:\"Calibri\",\"sans-serif\";}\nspan.MsoSubtleEmphasis\n\t{color:gray;\n\tfont-style:italic;}\nspan.HeaderChar\n\t{mso-style-name:\"Header Char\";\n\tmso-style-link:Header;}\nspan.FooterChar\n\t{mso-style-name:\"Footer Char\";\n\tmso-style-link:Footer;}\nspan.Heading2Char\n\t{mso-style-name:\"Heading 2 Char\";\n\tmso-style-link:\"Heading 2\";\n\tfont-family:\"Arial\",\"sans-serif\";\n\tcolor:black;\n\tfont-weight:bold;}\nspan.BodyText3Char\n\t{mso-style-name:\"Body Text 3 Char\";\n\tmso-style-link:\"Body Text 3\";\n\tfont-family:\"Verdana\",\"sans-serif\";\n\tcolor:black;}\nspan.BalloonTextChar\n\t{mso-style-name:\"Balloon Text Char\";\n\tmso-style-link:\"Balloon Text\";\n\tfont-family:\"Tahoma\",\"sans-serif\";}\nspan.HTMLPreformattedChar\n\t{mso-style-name:\"HTML Preformatted Char\";\n\tmso-style-link:\"HTML Preformatted\";\n\tfont-family:\"Courier New\";}\nspan.TitleChar\n\t{mso-style-name:\"Title Char\";\n\tmso-style-link:Title;\n\tfont-family:\"Bernard MT Condensed\",\"serif\";\n\tcolor:green;\n\tletter-spacing:.25pt;}\nspan.Heading3Char\n\t{mso-style-name:\"Heading 3 Char\";\n\tmso-style-link:\"Heading 3\";\n\tfont-family:\"Cambria\",\"serif\";\n\tcolor:#4F81BD;\n\tfont-weight:bold;}\nspan.Heading1Char\n\t{mso-style-name:\"Heading 1 Char\";\n\tmso-style-link:\"Heading 1\";\n\tfont-family:\"Cambria\",\"serif\";\n\tcolor:green;\n\tfont-weight:bold;}\nspan.SubtitleChar\n\t{mso-style-name:\"Subtitle Char\";\n\tmso-style-link:Subtitle;\n\tfont-family:\"Bookman Old Style\",\"serif\";\n\tletter-spacing:.75pt;\n\tfont-weight:bold;}\np.SampleIO, li.SampleIO, div.SampleIO\n\t{mso-style-name:SampleIO;\n\tmargin-top:0in;\n\tmargin-right:0in;\n\tmargin-bottom:0in;\n\tmargin-left:16.4pt;\n\tmargin-bottom:.0001pt;\n\tfont-size:12.0pt;\n\tfont-family:\"Courier 10 Pitch\";}\n.MsoChpDefault\n\t{font-size:10.0pt;}\n /* Page Definitions */\n @page Section1\n\t{size:8.5in 11.0in;\n\tmargin:1.0in 1.0in 1.0in 1.0in;}\ndiv.Section1\n\t{page:Section1;}\n /* List Definitions */\n ol\n\t{margin-bottom:0in;}\nul\n\t{margin-bottom:0in;}\n--\u003e\n\u003c/style\u003e \n \u003cp class\u003d\"MsoNormal\"\u003eGiven a dice with \u003cb\u003en\u003c/b\u003e sides, you have to find the expected number of times you have to throw that dice to see all its faces at least once. Assume that the dice is fair, that means when you throw the dice, the probability of occurring any face is equal.\u003c/p\u003e \n \u003cp class\u003d\"MsoNormal\"\u003eFor example, for a fair two sided coin, the result is 3. Because when you first throw the coin, you will definitely see a new face. If you throw the coin again, the chance of getting the opposite side is 0.5, and the chance of getting the same side is 0.5. So, the result is\u003c/p\u003e \n \u003cp class\u003d\"MsoNormal\" align\u003d\"center\" style\u003d\"text-align:center\"\u003e1 + (1 + 0.5 * (1 + 0.5 * ...))\u003c/p\u003e \n \u003cp class\u003d\"MsoNormal\" align\u003d\"center\" style\u003d\"text-align:center\"\u003e\u003d 2 + 0.5 + 0.5\u003csup\u003e2\u003c/sup\u003e + 0.5\u003csup\u003e3\u003c/sup\u003e + ...\u003c/p\u003e \n \u003cp class\u003d\"MsoNormal\" align\u003d\"center\" style\u003d\"text-align:center\"\u003e\u003d 2 + 1 \u003d 3\u003c/p\u003e \n "}},{"title":"Input","value":{"format":"HTML","content":" \n \u003cp class\u003d\"MsoNormal\"\u003eInput starts with an integer \u003cb\u003eT (\u003c/b\u003e\u003cb\u003e≤ 100)\u003c/b\u003e, denoting the number of test cases.\u003c/p\u003e \n \u003cp class\u003d\"MsoNormal\"\u003eEach case starts with a line containing an integer \u003cb\u003en (1 ≤ n ≤ 10\u003csup\u003e5\u003c/sup\u003e)\u003c/b\u003e.\u003c/p\u003e \n "}},{"title":"Output","value":{"format":"HTML","content":" \n \u003cp class\u003d\"MsoNormal\"\u003eFor each case, print the case number and the expected number of times you have to throw the dice to see all its faces at least once. Errors less than \u003cb\u003e10\u003csup\u003e-6\u003c/sup\u003e\u003c/b\u003e will be ignored.\u003c/p\u003e \n "}},{"title":"Sample Input","value":{"format":"HTML","content":" \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003e5\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003e1\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003e2\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003e3\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003e6\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003e100\u003c/span\u003e\u003c/p\u003e "}},{"title":"Sample Output","value":{"format":"HTML","content":" \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003eCase 1: 1\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003eCase 2: 3\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003eCase 3: 5.5\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003eCase 4: 14.7\u003c/span\u003e\u003c/p\u003e \u003cp class\u003d\"MsoNoSpacing\"\u003e\u003cspan style\u003d\"font-family:\u0026quot;Courier New\u0026quot;\"\u003eCase 5: 518.7377517640\u003c/span\u003e\u003c/p\u003e "}}]}