Flood Fill

题意翻译

$n$ 个方块排成一排，第 $i$ 个颜色为 $c_i$。定义一个颜色联通块 $[l,r]$ 当且仅当 $l$ 和 $r$ 之间（包括 $l,r$）所有方块的颜色相同。现在你可以选定一个起始位置 $p$，每次将 $p$ 所在颜色联通块的所有方块颜色改成另一种。这个操作可能将多个颜色联通块合并成一个。问最少要多少步，能让 $[1,n]$ 变成一个颜色联通块。 $1\le n,c_i\le 5000$。

题目描述

You are given a line of $ n $ colored squares in a row, numbered from $ 1 $ to $ n $ from left to right. The $ i $ -th square initially has the color $ c_i $ . Let's say, that two squares $ i $ and $ j $ belong to the same connected component if $ c_i = c_j $ , and $ c_i = c_k $ for all $ k $ satisfying $ i < k < j $ . In other words, all squares on the segment from $ i $ to $ j $ should have the same color. For example, the line $ [3, 3, 3] $ has $ 1 $ connected component, while the line $ [5, 2, 4, 4] $ has $ 3 $ connected components. The game "flood fill" is played on the given line as follows: - At the start of the game you pick any starting square (this is not counted as a turn). - Then, in each game turn, change the color of the connected component containing the starting square to any other color. Find the minimum number of turns needed for the entire line to be changed into a single color.

输入输出格式

输入格式

The first line contains a single integer $ n $ ( $ 1 \le n \le 5000 $ ) — the number of squares. The second line contains integers $ c_1, c_2, \ldots, c_n $ ( $ 1 \le c_i \le 5000 $ ) — the initial colors of the squares.

输出格式

Print a single integer — the minimum number of the turns needed.

输入输出样例

输入样例 #1

4
5 2 2 1

输出样例 #1

2

输入样例 #2

8
4 5 2 2 1 3 5 5

输出样例 #2

4

输入样例 #3

1
4

输出样例 #3

0

说明

In the first example, a possible way to achieve an optimal answer is to pick square with index $ 2 $ as the starting square and then play as follows: - $ [5, 2, 2, 1] $ - $ [5, 5, 5, 1] $ - $ [1, 1, 1, 1] $ In the second example, a possible way to achieve an optimal answer is to pick square with index $ 5 $ as the starting square and then perform recoloring into colors $ 2, 3, 5, 4 $ in that order. In the third example, the line already consists of one color only.