CF718E Matvey's Birthday

Today is Matvey's birthday. He never knows what to ask as a present so friends gave him a string $ s $ of length $ n $ . This string consists of only first eight English letters: 'a', 'b', $ ... $ , 'h'. First question that comes to mind is: who might ever need some string? Matvey is a special boy so he instantly found what to do with this string. He used it to build an undirected graph where vertices correspond to position in the string and there is an edge between distinct positions $ a $ and $ b $ ( $ 1

The first line of the input contains a single integer $ n $ ( $ 2

Print two integers — the diameter of the graph and the number of pairs of positions with the distance equal to the diameter.

Consider the second sample. The maximum distance is $ 2 $ . It's obtained for pairs $ (1,4) $ , $ (2,4) $ , $ (4,6) $ and $ (4,7) $ .