Cowdependence

Farmer John's $N$ $(1 \leq N \leq 10^5)$ cows have been arranged into a line. The $i$th cow has label $a_i$ ($1 \leq a_i \leq N$). A group of cows can form a friendship group if they all have the same label and each cow is within $x$ cows of all the others in the group, where $x$ is an integer in the range $[1,N]$. Every cow must be in exactly one friendship group.

For each $x$ from $1$ to $N$, calculate the minimum number of friendship groups that could have formed.

The first line consists of an integer $N$.

The next line contains $a_1 ... a_N$, the labels of each cow.

• Inputs 2-3: $N\le 5000$
• Inputs 4-7: $a_i\le 10$ for all $i$
• Inputs 8-11: No label appears more than $10$ times.
• Inputs 12-20: No additional constraints.

For each $x$ from $1$ to $N$, output the minimum number of friendship groups for that $x$ on a new line.

Here are examples of how to assign cows to friendship groups for $x=1$ and $x=2$ in a way that minimizes the number of groups. Each letter corresponds to a different group.