You are asked to design 10 flags with vertical stripes using three colors: blue, orange, yellow. You are asked not to have two neighboring stripes of the same color. You are also asked not to have yellow and orange stripes next to each other as it doesn't look nice. Your goal to minimize the number of stripes I need to use. So, you can make 3 different one-striped flags. You can make 4 different two-striped flags: blue-yellow, blue-orange, yellow-blue, orange-blue. You can make 6 different three-striped flags: blue-yellow-blue, yellow-blue-yellow, orange-blue-orange, blue-orange-blue, orange-blue-yellow, yellow-blue-orange. That is, you can make 13 different flags using 3 stripes at most.
Your task is, given the number of flags and the details of colors that may not be adjacent to each other (a color always has atleast one forbidden neighbor namely itself),return the minimum number of stripes you need to design the given number of different flags using at most that amount of stripes.
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