문제

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.

입력

The first line consists of an integer $N$.

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

출력

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

예제 입력 1

9
1 1 1 9 2 1 2 1 1

예제 출력 1

7
5
4
4
4
4
4
3
3

점수

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.