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Old timers of Summer Informatics School can remember previous camps in which each student was given a drink of his choice on the vechorka (late-evening meal). Or may be the story was more complicated?
There are $$$n$$$ students living in a building, and for each of them the favorite drink $$$a_i$$$ is known. So you know $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$, where $$$a_i$$$ ($$$1 \le a_i \le k$$$) is the type of the favorite drink of the $$$i$$$-th student. The drink types are numbered from $$$1$$$ to $$$k$$$.
There are infinite number of drink sets. Each set consists of exactly two portions of the same drink. In other words, there are $$$k$$$ types of drink sets, the $$$j$$$-th type contains two portions of the drink $$$j$$$. The available number of sets of each of the $$$k$$$ types is infinite.
You know that students will receive the minimum possible number of sets to give all students exactly one drink. Obviously, the number of sets will be exactly $$$\lceil \frac{n}{2} \rceil$$$, where $$$\lceil x \rceil$$$ is $$$x$$$ rounded up.
After students receive the sets, they will distribute their portions by their choice: each student will get exactly one portion. Note, that if $$$n$$$ is odd then one portion will remain unused and the students' teacher will drink it.
What is the maximum number of students that can get their favorite drink if $$$\lceil \frac{n}{2} \rceil$$$ sets will be chosen optimally and students will distribute portions between themselves optimally?
The first line of the input contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n, k \le 1\,000$$$) — the number of students in the building and the number of different drinks.
The next $$$n$$$ lines contain student's favorite drinks. The $$$i$$$-th line contains a single integer from $$$1$$$ to $$$k$$$ — the type of the favorite drink of the $$$i$$$-th student.
Print exactly one integer — the maximum number of students that can get a favorite drink.
5 3 1 3 1 1 2
4
10 3 2 1 3 2 3 3 1 3 1 2
9
In the first example, students could choose three sets with drinks $$$1$$$, $$$1$$$ and $$$2$$$ (so they will have two sets with two drinks of the type $$$1$$$ each and one set with two drinks of the type $$$2$$$, so portions will be $$$1, 1, 1, 1, 2, 2$$$). This way all students except the second one will get their favorite drinks.
Another possible answer is sets with drinks $$$1$$$, $$$2$$$ and $$$3$$$. In this case the portions will be $$$1, 1, 2, 2, 3, 3$$$. Then all the students except one will gain their favorite drinks. The only student that will not gain the favorite drink will be a student with $$$a_i = 1$$$ (i.e. the first, the third or the fourth).
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Provedor Codeforces
Código CF1195A
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Datas 09/05/2023 09:50:00
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