{"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\u003eGiven an array a of N integers a1, a2, a3, ... aN you have to find the longest alternating sub-sequence of this array.\u003c/p\u003e\r\n\u003cp\u003eAn alternating sequence b1, b2 ... bk, k\u0026gt;\u003d1 is a sequence that has the 2 following properties:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e |b1| \u0026lt; |b2| \u0026lt; |b3| \u0026lt; ... \u0026lt; |bk|\u003c/li\u003e\r\n\u003cli\u003eThe signs alternate between adjacent elements, i.e., if b1 \u0026gt; 0 then b2 \u0026lt; 0, b3 \u0026gt; 0 and so on. Alternatively, if b1 \u0026lt; 0, then b2 \u0026gt; 0, b3 \u0026lt; 0 and so on.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eA sub sequence of array a is a sequence obtained by dropping some elements of the array a. Here is the formal definition.\u003c/p\u003e\r\n\u003cp\u003eIt is guaranteed that the array a contains no element equal to 0.\u003c/p\u003e\r\n\u003ch3\u003eConstraints\u003c/h3\u003e\r\n\u003cp\u003e\r\n1 \u0026lt;\u003d N \u0026lt;\u003d 5000\u003cbr\u003e\r\n|ai| \u0026lt;\u003d 10^9, ai not equal to 0.\u003c/p\u003e\r\n\u003ch3\u003eInput\u003c/h3\u003e\r\n\u003cp\u003eThe first line contains a single integer N, denoting the size of the array. The next line contains N integers, denoting the array a.\r\n\r\n\u003c/p\u003e\u003ch3\u003eOutput\u003c/h3\u003e\r\n\u003cp\u003ePrint a single integer - the length of the longest alternating sub-sequence.\u003c/p\u003e\r\n\r\n\u003ch3\u003eExample\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\u003e8\r\n1 2 -2 -3 5 -7 -8 10\r\n\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\r\n\u003ch3\u003eExplanation\u003c/h3\u003e\r\n\u003cp\u003eOne of the longest alternating subsequence is\u003c/p\u003e\r\n\u003cpre\u003e 1 -2 5 -7 10\u003c/pre\u003e\r\n\n\u003c/div\u003e"}}]}