Problem:
Score : 400 points

Problem Statement

Snuke has decided to play a game using cards.
He has a deck consisting of N cards. On the i-th card from the top, an integer A_i is written.

He will perform the operation described below zero or more times, so that the values written on the remaining cards will be pairwise distinct. Find the maximum possible number of remaining cards. Here, N is odd, which guarantees that at least one card can be kept.

Operation: Take out three arbitrary cards from the deck. Among those three cards, eat two: one with the largest value, and another with the smallest value. Then, return the remaining one card to the deck.

Constraints

3 ≦ N ≦ 10^{5}

N is odd.

1 ≦ A_i ≦ 10^{5}

A_i is an integer.

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 A_3 ... A_{N}

Output

Print the answer.

Sample Input 1

5
1 2 1 3 7

Sample Output 1

3

One optimal solution is to perform the operation once, taking out two cards with 1 and one card with 2. One card with 1 and another with 2 will be eaten, and the remaining card with 1 will be returned to deck. Then, the values written on the remaining cards in the deck will be pairwise distinct: 1, 3 and 7.

Sample Input 2

15
1 3 5 2 1 3 2 8 8 6 2 6 11 1 1

Sample Output 2

7

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using static kyoupuro.Input;
using static kyoupuro.MyMath;

namespace kyoupuro {

    class MainClass {

        public static void Main() {
            var N = NextInt();
            var A = IntList();

            var count = A.Distinct().Count();

            Console.WriteLine(count - 1 + count % 2);
        }
    }

    class MyMath {
        public const long mod = 1000000007;

        public static long Gcd(long a, long b) {
            return b == 0 ? a : Gcd(b, a % b);
        }

        public static List<long> Factor(long n) {
            var list = new List<long>();
            n = DivideToLimit(n, 2, list);
            n = DivideToLimit(n, 3, list);
            long sqrt = Sqrt(n);
            for (int i = 5; i <= n && i <= sqrt; i += 4) {
                n = DivideToLimit(n, i, list);
                i += 2;
                n = DivideToLimit(n, i, list);
            }
            if (n > 1) list.Add(n);
            return list;
        }

        public static long Sqrt(long n) {
            if (n < 0) return 0;
            long a = 0, tmp = 0, b = 0;
            for (int i = 62; i >= 0; i -= 2) {
                tmp = (b << 1) + 1 <= (n >> i) ? 1 : 0;
                a = a << 1 | tmp;
                n -= (((b << 1) + 1) * tmp) << i;
                b = (b << 1) + tmp + tmp;
            }
            return a;
        }

        static long DivideToLimit(long divisor, long dividend, List<long> list) {
            while (divisor % dividend == 0) {
                list.Add(dividend);
                divisor /= dividend;
            }
            return divisor;
        }
    }

    public class PriorityQueue<T> : IEnumerable<T> {

        readonly List<T> _data = new List<T>();
        readonly IComparer<T> _comparer;

        public PriorityQueue(IComparer<T> comparer) {
            _comparer = comparer;
        }

        public PriorityQueue() : this(Comparer<T>.Default) { }

        public void Enqueue(T item) {
            _data.Add(item);

            int childID = _data.Count - 1;
            int parentID = (childID - 1) / 2;

            while (childID > 0 && _comparer.Compare(_data[parentID], _data[childID]) > 0) {
                Swap(parentID, childID);
                childID = parentID;
                parentID = (parentID - 1) / 2;
            }
        }

        public T Dequeue() {
            var first = _data.First();
            _data[0] = _data.Last();
            _data.RemoveAt(_data.Count - 1);

            int parentID = 0;
            int childID = parentID * 2 + 2;
            if (childID >= _data.Count || _comparer.Compare(_data[childID], _data[childID - 1]) > 0) childID--;

            while (childID < _data.Count && _comparer.Compare(_data[parentID], _data[childID]) > 0) {
                Swap(parentID, childID);
                parentID = childID;
                childID = parentID * 2 + 2;
                if (childID >= _data.Count || _comparer.Compare(_data[childID], _data[childID - 1]) > 0) childID--;
            }

            return first;
        }

        void Swap(int parent, int child) {
            var tmp = _data[parent];
            _data[parent] = _data[child];
            _data[child] = tmp;
        }

        public T Peek() { return _data[0]; }
        public int Count => _data.Count;

        public IEnumerator<T> GetEnumerator() {
            foreach(var item in _data) {
                yield return item;
            }
        }

        IEnumerator IEnumerable.GetEnumerator() {
            return GetEnumerator();
        }
    }

    class Input {
        static IEnumerator<string> enumerator = new string[] { }.AsEnumerable().GetEnumerator();

        public static string Line() {
            return Console.ReadLine();
        }

        public static int NextInt() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
            }
            return int.Parse(enumerator.Current);
        }

        public static long NextLong() {
            while (!enumerator.MoveNext()) {
                enumerator = StrArr().AsEnumerable().GetEnumerator();
            }
            return long.Parse(enumerator.Current);
        }

        public static string[] StrArr() {
            return Line().Split(' ');
        }

        public static List<int> IntList() {
            return StrArr().Select(int.Parse).ToList();
        }

        public static List<long> LongList() {
            return StrArr().Select(long.Parse).ToList();
        }
    }
}