The file sunspots.txt contains the annual average number of sunspots observed on the surface of the sun from $1700-2023.($The first value is for the year $1700,$ the second value is for the year $1701,$ etc.$)$

Generate a time$-$series plot showing how the number of sunspots on the surface of the sun varies over time. You will notice a cyclical pattern. By visual inspection, estimate the length of the sunspot cycle, that is$,$ the average number of years from peak to peak.

Additional requirements:

$$ Plot all points as blue dots using the $.$ Marker, except when the year is between $1790$ and $1830.$ During these years, plot the points using the $$x$$ marker and make them red instead of blue. This period is known as the $$Dalton Minimum$$

$$ Before plotting add the line: plt$.$figure$($figsize$=(20,2),$ dpi$=200)$

This creates a $20$x$2$ inch plot with a resolution of $200$ dots $($pixels$)$ per inch. Experiment with the size parameters to obtain the clearest results.

$$ Automatically save your plot to a file with the statement: plt$.$savefig$("$sunspots$.$png$",$ bbox$\_$inches$=$"tight"$)$

Be sure to include this line before plt$.$show$().$ Otherwise, your saved file will be blank.

$$ Overlay a grid and be sure to include helpful axis titles.

$$ Manually count the number of peaks. You do NOT need to write any code to detect the peak years. Estimate the solar cycle length by manually counting the number of peaks over a given number of years. Specifically:

cycle$\_$length $=$ years $/($peaks $1)$

Thought question: Why do we subtract $1$ in the denominator? Report your estimate to one decimal place in the header of your program. Document the number of peaks and the # of years that were used to derive your estimate. You do not need to answer the thought question, but you may.