{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":" You are given lengths of sides of some polygon. You must find the infimum of the possible areas of simple polygons with such side lengths. \u003ci\u003eInfimum\u003c/i\u003e of a set of real numbers \u003ci\u003eA\u003c/i\u003e is the exact upper bound of the set \u003ci\u003eL\u003c/i\u003e of all real numbers \u003ci\u003ey\u003c/i\u003e such that for any \u003ci\u003ex\u003c/i\u003e ∈ \u003ci\u003eA\u003c/i\u003e holds \u003ci\u003ey\u003c/i\u003e ≤ \u003ci\u003ex\u003c/i\u003e.\u003cbr\u003eA \u003ci\u003esimple polygon\u003c/i\u003e is a polygon without self-intersections and self-touchings.\u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eInput\u003c/b\u003e\u003c/div\u003eThe first line contains integer \u003ci\u003en\u003c/i\u003e, 3 ≤ \u003ci\u003en\u003c/i\u003e ≤ 10 — the number of sides of the polygon. The second line contains \u003ci\u003en\u003c/i\u003e integers \u003ci\u003ea\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e,..., \u003ci\u003ea\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e, such that \u003cimg src\u003d\"CDN_BASE_URL/9bfcfa2c04f927659b197ee6d71211ae?v\u003d1716043647\" style\u003d\"vertical-align: text-bottom;top: -2.0px;max-width: 100.0%;max-height: 100.0%;\"\u003e for any 1 ≤ \u003ci\u003ei\u003c/i\u003e ≤ \u003ci\u003en\u003c/i\u003e (this means that there exists a simple polygon with sides \u003ci\u003ea\u003c/i\u003e\u003csub\u003e1\u003c/sub\u003e, \u003ci\u003ea\u003c/i\u003e\u003csub\u003e2\u003c/sub\u003e,..., \u003ci\u003ea\u003c/i\u003e\u003csub\u003e\u003ci\u003en\u003c/i\u003e\u003c/sub\u003e. Also, 1 ≤ \u003ci\u003ea\u003c/i\u003e\u003csub\u003e\u003ci\u003ei\u003c/i\u003e\u003c/sub\u003e ≤ 100.\u003cbr\u003e\u003cdiv align\u003d\"left\" style\u003d\"margin-top: 1.0em;\"\u003e\u003cb\u003eOutput\u003c/b\u003e\u003c/div\u003eOutput one real number — the answer to the problem. Your answer will be considered correct if absolute or relative error is less than 10\u003csup\u003e-6\u003c/sup\u003e.\u003cbr\u003e"}},{"title":"Sample 1","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\n3 4 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e6.0000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 2","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\n8 4 3 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4.4721359550\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 3","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\n5 5 5 5 5 5 5 5 5 5\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.0000000000\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}