A852. Even More Odd Photos--Bronze

Farmer John is yet again trying to take a photograph of his $N$ cows ($2 \leq
N \leq 1000$).
Each cow has an integer "breed ID" number in the range $1 \ldots 100$. Farmer
John has a very peculiar idea in mind for his photo: he wants to partition all
the cows into disjoint groups (in other words, place each cow in exactly one
group) and then line up the groups so the sum of the breed IDs of the cows in
the first group is even, the sum of the IDs in the second group is odd, and so
on, alternating between even and odd.
What is the maximum possible number of groups Farmer John can form?

The first line of input contains $N$. The next line contains $N$ space-
separated integers giving the breed IDs of the $N$ cows.

The maximum possible number of groups in Farmer John's photo. It can be shown
that at least one feasible grouping exists.

In this example, one way to form the maximum number of three groups is as
follows. Place 1 and 3 in the first group, 5, 7, and 9 in the second group,
and 11 and 13 in the third group.