The multi-layered pie-chart below shows the sales of LED television sets for a big retail electronics outlet during $2016$ and $2017$. The outer layer shows the monthly sales during this period, with each label showing the month followed by sales figure of that month. For some months, the sales figures are not given in the chart. The middle-layer shows quarter-wise aggregate sales figures (in some cases, aggregate quarter-wise sales numbers are not given next to the quarter). The innermost layer shows annual sales. It is known that the sales figures during the three months of the second quarter (April, May, June) of $2016$ form an arithmetic progression, as do the three monthly sales figures in the fourth quarter (October, November, December) of that year.
In which quarter of $2017$ was the percentage increase in sales from the same quarter of $2016$ the highest?