A907.Modern Art 2--Gold

Having become bored with standard 2-dimensional artwork (and also frustrated
at others copying her work), the great bovine artist Picowso has decided to
switch to a more minimalist, 1-dimensional style.
Although, her paintings can now be described by a 1-dimensional array of
colors of length $N$ ($1 \leq N \leq 100,000$), her painting style remains
unchanged: she starts with a blank canvas and layers upon it a sequence of
"rectangles" of paint, which in this 1-dimensional case are simply intervals.
She uses each of the colors $1 \ldots N$ exactly once, although just as
before, some colors might end up being completely covered up by the end.
To Picowso's great dismay, her competitor Moonet seems to have figured out how
to copy even these 1-dimensional paintings, using a similar strategy to the
preceding problem: Moonet will paint a set of disjoint intervals, wait for
them to dry, then paint another set of disjoint intervals, and so on. Moonet
can only paint at most one interval of each color over the entire process.
Please compute the number of such rounds needed for Moonet to copy a given
1-dimensional Picowso painting.

The first line of input contains $N$, and the next $N$ lines contain an
integer in the range $0 \ldots N$ indicating the color of each cell in the
1-dimensional painting (0 for a blank cell).

Please output the minimum number of rounds needed to copy this painting, or -1
if this could not have possibly been an authentic work of Picowso (i.e., if
she could not have painted it using a layered sequence of intervals, one of
each color).

In this example, the interval of color 1 must be painted in an earlier round
than the intervals of colors 4 and 5, so at least two rounds are needed.