4292: Till I Collapse
内存限制：256 MB
时间限制：2 S
题面：传统
评测方式：文本比较
上传者：
提交：1
通过：1
题目描述
time limit per test
2 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputRick and Morty want to find MR. PBH and they can't do it alone. So they need of Mr. Meeseeks. They Have generated n Mr. Meeseeks, standing in a line numbered from 1 to n. Each of them has his own color. i-th Mr. Meeseeks' color is ai.
Rick and Morty are gathering their army and they want to divide Mr. Meeseeks into some squads. They don't want their squads to be too colorful, so each squad should have Mr. Meeseeks of at most k different colors. Also each squad should be a continuous subarray of Mr. Meeseeks in the line. Meaning that for each 1≤i≤e≤j≤n, if Mr. Meeseeks number i and Mr. Meeseeks number j are in the same squad then Mr. Meeseeks number e should be in that same squad.
Also, each squad needs its own presidio, and building a presidio needs money, so they want the total number of squads to be minimized.
Rick and Morty haven't finalized the exact value of k, so in order to choose it, for each k between 1 and n (inclusive) need to know the minimum number of presidios needed.
Rick and Morty are gathering their army and they want to divide Mr. Meeseeks into some squads. They don't want their squads to be too colorful, so each squad should have Mr. Meeseeks of at most k different colors. Also each squad should be a continuous subarray of Mr. Meeseeks in the line. Meaning that for each 1≤i≤e≤j≤n, if Mr. Meeseeks number i and Mr. Meeseeks number j are in the same squad then Mr. Meeseeks number e should be in that same squad.
Rick and Morty haven't finalized the exact value of k, so in order to choose it, for each k between 1 and n (inclusive) need to know the minimum number of presidios needed.
Input
The first line of input contains a single integer n (1≤n≤105) − number of Mr. Meeseeks.The second line contains n integers a1,a2,...,an separated by spaces (1≤ai≤n) − colors of Mr. Meeseeks in order they standing in a line.
Output
In the first and only line of input print n integers separated by spaces. i-th integer should be the minimum number of presidios needed if the value of k is i.Examples
Input
5
1 3 4 3 3
Output
4 2 1 1 1
Input
8
1 5 7 8 1 7 6 1
Output
8 4 3 2 1 1 1 1
Note
For the first sample testcase, some optimal ways of dividing army into squads for each k are:- [1],[3],[4],[3,3]
- [1],[3,4,3,3]
- [1,3,4,3,3]
- [1,3,4,3,3]
- [1,3,4,3,3]
- [1],[5],[7],[8],[1],[7],[6],[1]
- [1,5],[7,8],[1,7],[6,1]
- [1,5,7],[8],[1,7,6,1]
- [1,5,7,8],[1,7,6,1]
- [1,5,7,8,1,7,6,1]
- [1,5,7,8,1,7,6,1]
- [1,5,7,8,1,7,6,1]
- [1,5,7,8,1,7,6,1]
输入样例 复制
输出样例 复制