【2017青岛网络赛】hdu 6212 Zuma 1007 区间dp

Problem Description
Think about the Zuma Game. You have a row of at most  200  black(0) or white(1) balls on the table at the start. Each three consecutive balls never share the same colour. You also have infinite amount of black and white balls in your hand. On each turn, you can choose a ball in your hand and insert it into the row, including the leftmost place and the rightmost place. Then, if there is a group of three of more balls in the same colour touching, remove these balls. Keep doing this until no more balls can be removed.
Find the minimal balls you have to insert to remove all the balls on the table.
 

Input
The first line of input contains an integer 
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