Global Warming

A scientist wants to study how a rising sea level changes the landform, and above all how it changes the number of islands. He starts with one-dimensional worlds. A one-dimensional world is a sequence of non-negative integers $\langle h_0, h_1, \ldots, h_{n-1} \rangle$, where $h_i$ is the altitude at location $i$. The figure below shows the world given by the sequence $\langle 5, 6, 1, 3, 2, 9, 8 \rangle$.

If the sea level is at altitude $2.5$, there are 3 islands: the first two columns, the fourth column, and the last two columns. If the sea level is at altitude $3.5$, there are only 2 islands. When the sea level is at altitude $x$, land at altitude $x$ counts as submerged, so at sea level $3$ there are again 2 islands. In this world 3 is the largest number of islands over all sea levels.

The sea level $x$ is any real number, and an island is a maximal run of side by side columns that stay above the water. Given a one-dimensional world, find the largest number of islands over all sea levels.

Your program reads from standard input. The first line contains the integer $n$, the number of integers in the sequence. Each of the next $n$ lines contains one integer, and these $n$ numbers form the sequence $\langle h_0, h_1, \ldots, h_{n-1} \rangle$. Every number in the sequence is non-negative and smaller than $2^{30}$.

Your program writes to standard output one integer, the largest number of islands.