Alice has n candies, where the ith candy is of type candies[i]. Alice noticed that she started to gain weight, so she visited a doctor.

The doctor advised Alice to only eat n/2 of the candies she has (n is always even). Alice likes her candies very much, and she wants to eat the maximum number of different types of candies while still following the doctor's advice.

Given the integer array candies of length n, return the maximum number of different types of candies she can eat if she only eats n/2 of them.

Example 1:

Input: candies = [1,1,2,2,3,3] Output: 3

Half of the candies is three, there are also three types of candies, since there is no conflict, Alice can eat three different types of candies.

Example 2:

Input: candies = [1,1,2,3] Output: 2

There are three different types of candies, however doctor advice limits it to two.

Example 3:

Input: candies = [5,5,5,5,5,5] Output: 1

While Alice can eat up to three given the doctor's advice, there is only one kind of candy.