Algorithm that balances the number of elements in a subinterval of an array? -

lets have array 4 different types of elements.

1 1 2 3 1 2 2 3 3 4 4 1. 

i want find longest subinterval results in equal number of each elements , largest total number of elements.

in case,

1 1 2 3 1 2 2 3 3

because results in 3 twos, 3 threes, , 3 ones.

i believe sort of modified dynamic programming, or requires prefix sums not sure. can give me insight on how start?

#!/usr/bin/env python  #the demo data set = [1,1,2,3,1,2,2,3,3,4,4,1]  #function map counts of values in set def map(x):         ret = {}         v in x:                 if v not in ret.keys():                         ret.update({v:0})                 ret[v] += 1         return ret  #function check if counts in map same def checkmap(x):         val = none         k,v in x.items():                 if val != none , v != val:                         return false                 else:                         val=v         return true  #determine initial counts counts = map(set)  #now step end index start ix in range(len(set) - 1, 0, -1):         val = set[ix]         counts[val] += -1         if counts[val] == 0:                 del counts[val]         if checkmap(counts):                 print "condition reached, largest subset is:",set[0:ix]                 break