{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n .markdown img {\n max-width: 900px;\n display: block;\n margin: 10px auto;\n }\n .markdown code {\n display: inline-block;\n padding: 0 4px;\n margin: 0;\n background-color: rgba(0, 0, 0, 0.04);\n border-radius: 3px;\n font-weight: bold;\n }\n .markdown pre code {\n display: block;\n padding: 20px;\n font-weight: normal;\n }\n .markdown table {\n width: 100%;\n table-layout: fixed;\n border-collapse: collapse;\n }\n .markdown table th {\n font-size: 13px;\n text-align: left;\n padding: 10px;\n border: 1px solid #e0e0e0;\n background: #f1f1f1;\n }\n .markdown table td {\n font-size: 14px;\n padding: 5px 10px;\n border: 1px solid #e0e0e0;\n }\n .markdown-form-widget .markdown-notice p {\n padding: 0;\n margin: 0;\n color: #999999;\n font-size: 11px;\n }\n\u003c/style\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"latex latex-raw\"\u003e\u003cimg src\u003d\"CDN_BASE_URL/cbafe667dcdd849748f49b4b4824ce40?v\u003d1714529870\"\u003e\u003cp\u003e\u003c/p\u003e\n\n\u003cp\u003e\u003cstrong\u003eLCM\u003c/strong\u003e (Least Common Multiple) of a set of integers is defined as the minimum number, which is a multiple of all integers in that set. It is interesting to note that any positive integer can be expressed as the \u003cstrong\u003eLCM\u003c/strong\u003e of a set of positive integers. For example \u003cstrong\u003e12\u003c/strong\u003e can be expressed as the \u003cstrong\u003eLCM\u003c/strong\u003e of \u003cstrong\u003e1\u003c/strong\u003e, \u003cstrong\u003e12\u003c/strong\u003e or \u003cstrong\u003e12\u003c/strong\u003e, \u003cstrong\u003e12\u003c/strong\u003e or \u003cstrong\u003e3\u003c/strong\u003e, \u003cstrong\u003e4\u003c/strong\u003e or \u003cstrong\u003e4\u003c/strong\u003e, \u003cstrong\u003e6\u003c/strong\u003e or \u003cstrong\u003e1\u003c/strong\u003e, \u003cstrong\u003e2\u003c/strong\u003e, \u003cstrong\u003e3\u003c/strong\u003e, \u003cstrong\u003e4\u003c/strong\u003e etc.\u003c/p\u003e\n\n\u003cp\u003eIn this problem, you will be given a positive integer \u003cstrong\u003en\u003c/strong\u003e. You have to find a set of at least two positive integers whose \u003cstrong\u003eLCM\u003c/strong\u003e is \u003cstrong\u003en\u003c/strong\u003e. As there exists an infinite number of such sequences, you have to pick the sequence whose summation of elements is minimum. We will be quite happy if you just print the summation of the elements of this set. So, for \u003cstrong\u003en\u003c/strong\u003e \u003d \u003cstrong\u003e12\u003c/strong\u003e, you should print \u003cstrong\u003e4 + 3 \u003d 7\u003c/strong\u003e as \u003cstrong\u003eLCM\u003c/strong\u003e of \u003cstrong\u003e4\u003c/strong\u003e and \u003cstrong\u003e3\u003c/strong\u003e is \u003cstrong\u003e12\u003c/strong\u003e and \u003cstrong\u003e7\u003c/strong\u003e is the minimum possible summation.\u003c/p\u003e\n\n\u003cp\u003e\u003c/p\u003e\u003ch2\u003eInput\u003c/h2\u003e\u003cp\u003e\u003c/p\u003e\n\n\u003cp\u003eInput contains at most \u003cstrong\u003e100\u003c/strong\u003e test cases. Each test case consists of a positive integer \u003cstrong\u003en\u003c/strong\u003e (\u003cstrong\u003e1\u003c/strong\u003e\u003cem\u003e ≤ \u003c/em\u003e\u003cstrong\u003en\u003c/strong\u003e\u003cem\u003e ≤ \u003c/em\u003e\u003cstrong\u003e2^31\u003c/strong\u003e -- \u003cstrong\u003e1\u003c/strong\u003e). Input is terminated by a case where \u003cstrong\u003en\u003c/strong\u003e \u003d \u003cstrong\u003e0\u003c/strong\u003e. This case should not be processed. There can be at most \u003cstrong\u003e100\u003c/strong\u003e test cases.\u003c/p\u003e\n\n\u003cp\u003e\u003c/p\u003e\u003ch2\u003eOutput\u003c/h2\u003e\u003cp\u003e\u003c/p\u003e\n\n\u003cp\u003eOutput of each test case should consist of a line starting with \"\u003cstrong\u003eCase #:\u003c/strong\u003e \" where \u003cstrong\u003e#\u003c/strong\u003e is the test case number. It should be followed by the summation as specified in the problem statement. Look at the output for sample input for details.\u003c/p\u003e\n\n\u003c/div\u003e"}},{"title":"Example","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\u003e12\n10\n5\n0\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1: 7\nCase 2: 7\nCase 3: 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}