After exploring Mars, NASA has discovered a mysterious kind of extra-terrestrial creature residing on the planet thought to be deserted. The creature is actually a collective body of millions of smaller individual, each comprising only of a few cells. Due to its form and its means of moving, the scientists dub it "Slime".

NASA decided to further investigate the knowledge level of the creature by sending messages to the living and observing its reaction, i.e. whether it knows of geometry by sending a figure of pythagorean theorem graphicalized, and whether it knows of physics by illustrating the gravity equation. To test that whether they knows of programmin, the scientists decided to use the improved version of "longest increasing subsequence" - the so-called "longest jumping subsequence".

A subsequence is defined by a subset of the elements of the original sequence arranged in the same order as they appear originally. A "jumping subsequence", as its name suggests, is simply a sequence whose relations between two adjacent elements alternates between "strictly increasing" and "strictly decreasing". For example, the sequence <2, 3, 2, 4, 1, 2, 1> and <4, 1, 5, 2, 6, 3> and <5, 8> are all legal "jumping subsequence". Being a Slime of much wisdom (certainly you are), your task here is to solve the "longest jumping subsequence" problem. Given a sequence of integer numbers, find the length of the longest subsequence in it that is jumping.