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 NN (1 \leq N \leq 100,0001≤N≤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 N1…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 NN, and the next NN lines contain an integer in the range 0 \ldots N0…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.
0 1 1 1 1 3 3
0 1 4 5 1 3 3
感谢 @ Night_Aurora 贡献翻译
一道大水题（容易想得太复杂了），一种颜色只能用一次，而且必须连续涂，那么被分开来的就一定是被其他颜色覆盖了的，而这段“其他颜色”又可以被覆盖，而且颜色块不能相交（例如0 1 2 1 2就是非法的），我们的问题就转化成了，最大有多少层嵌套的问题。