{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n #problem-body \u003e pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv id\u003d\"problem-body\"\u003e\n\t\u003cp\u003eFarmer John\u0027s owns N cows (2 \u0026lt;\u003d N \u0026lt;\u003d 20), where cow i produces M(i) units of milk each day (1 \u0026lt;\u003d M(i) \u0026lt;\u003d 100,000,000).\u003c/p\u003e\r\n\u003cp\u003eFJ wants to streamline the process of milking his cows every day, so he installs a brand new milking machine in his barn.\u003c/p\u003e\r\n\u003cp\u003eUnfortunately, the machine turns out to be far too sensitive: it only works properly if the cows on the left side of the barn have the exact same total milk output as the cows on the right side of the barn!\u003c/p\u003e\r\n\u003cp\u003eLet us call a subset of cows \"balanced\" if it can be partitioned into two groups having equal milk output.\u003c/p\u003e\r\n\u003cp\u003eSince only a balanced subset of cows can make the milking machine work, FJ wonders how many subsets of his N cows are balanced.\u003c/p\u003e\r\n\u003cp\u003ePlease help him compute this quantity.\u003c/p\u003e\r\n\u003ch3\u003eInput\u003c/h3\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eLine 1: The integer N.\u003c/li\u003e\r\n\u003cli\u003eLines 2..1+N: Line i+1 contains M(i).\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003ch3\u003eOutput\u003c/h3\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eLine 1: The number of balanced subsets of cows.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\r\n\u003ch3\u003eSample\u003c/h3\u003e\r\n\u003cdiv\u003e\u003ctable class\u003d\"vjudge_sample\"\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\r\n1\r\n2\r\n3\r\n4\r\n\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\r\n\r\n\u003ch3\u003eExplanation\u003c/h3\u003e\r\n\u003cp\u003eThere are 4 cows, with milk outputs 1, 2, 3, and 4.\u003c/p\u003e\r\n\u003cp\u003eThere are three balanced subsets: the subset {1,2,3}, which can be partitioned into {1,2} and {3}, the subset {1,3,4}, which can be partitioned into {1,3} and {4}, and the subset {1,2,3,4} which can be partitioned into {1,4} and {2,3}.\u003c/p\u003e\r\n\n\u003c/div\u003e"}}]}