Problem 1916. GJam 2013 Veterans: Hedge

This Challenge is derived from Hedgemony. This is the Large data set with N<=1000.

The GJam story goes that the Baron trims the bushes(1:N) starting with bush 2 thru the next to last bush(N-1). A bush is trimmed to the average of the adjacent bushes. If the bush is less than the adjacent average the bush is left alone. Report the final Height of the next to last bush following its trimming.

Input: hin , Vector length N<=1000 with values between 1 and 1000.

Output: hout , Final Trimmed Height of the next to last bush (accuracy <2e-4)

Examples: [hin] [hout]

[1 2 3 6 7] [5.000000]
[5 8 9 9 9] [8.500000]
[1 2 2 2 2 2] [1.937500]

Commentary:

1) Best Time: 7 minutes
2) Solved by 27 of 32