This Challenge is derived from GJam 2013 Veterans Ocean View. This is the Small data set witn N<=50 and Q<=4, guaranteed.
The GJam story goes that as Supreme Ruler you are annoyed by complaints of non-ocean views on a hillside. To resolve the issue a minimum number of homes will be removed to provide a maximum number of ocean view homes. The Elevation of the homes should monotonically increase, no equal values, from element 1 thru the end.
Succinct Challenge statement: Given a vector create the maximum length monotonically increasing vector by removing values. Report the number of values removed.
Input: V , Vector length N<=50 with values 1 thru 1000.
Output: Q , minimum quantity of removed values to produce a valid vector [0:4]
Examples: [V] [Q]
[1 4 3 3]  for [1 4] or [1 3] [1 2 3 4 5]  [4 3 2 1] 
1) The GJam Small test suite is not robust 2) nchoosek(50,4) is too slow for Cody and the 100 cases 3) The Large test suite is N<=1000 with some delete cases >4 4) A Good Algorithm that solves the Large case is usually best to pursue 5) GJam Competition allows one Large submission within 10 minutes of download 6) <Large Suite Challenge>