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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <boost/range/algorithm.hpp>
#include <boost/range/numeric.hpp>
#include <boost/integer/common_factor.hpp>
#include <boost/integer/common_factor_rt.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>

using std::string;
using std::vector;
using std::set;
using std::multiset;
using std::unordered_set;
using std::map;
using std::multimap;
using std::unordered_map;
using std::pair;
using std::cin;
using std::cout;

using boost::multiprecision::cpp_int;
using cpp_dec_float_1000 = boost::multiprecision::number<boost::multiprecision::cpp_dec_float<1000, boost::int128_type>>;

typedef uintmax_t    ull;
typedef intmax_t     ll;
typedef uint64_t     ul;
typedef uint32_t     ui;
typedef uint8_t      uc;

constexpr char CRLF  = '\n';
constexpr char SPACE = ' ';
constexpr char VECTOR_COUT_SEPARATOR = SPACE;
constexpr ll INF = 1000'000'007;
constexpr int MOD = 1000'000'007;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }
template<class T> std::ostream& operator<< (std::ostream& os, const std::vector<T>& vc) { for(auto it = vc.begin(); it != vc.end(); ++it) { if (std::next(it) == vc.end()) os << *it; else os << *it << VECTOR_COUT_SEPARATOR; } return os; }
template<class T1, class T2> inline std::ostream & operator<< (std::ostream & os, const std::pair<T1, T2> & p) { return os << p.first << ' ' << p.second; }
template<class T> T modinv(T a, T m) { T b = m, u = 1, v = 0; while (b) { T t = a / b; a -= t * b; boost::swap(a, b); u -= t * v; boost::swap(u, v); } u %= m; if (u < 0) u += m; return u; }
template<class T> inline bool isSosuu(const T& n) { if (n == T(1)) { return false; } for (T i = 2; i*i <= n; ++i) { if (n % i == 0) { return false; } } return true; }
template<class T> vector<vector<T>> split (const vector<T>& S, T delim) { vector<vector<T>> ret{}; vector<T> buff{}; for (auto c : S) { if (c == delim) { if (!buff.empty()) ret.push_back(buff); buff.clear(); } else { buff.push_back(c); } } if (!buff.empty()) ret.push_back(buff); return ret; }
template<class T> inline void printYesNo(const T& t) { cout << (t ? "Yes" : "No") << CRLF; }
template<class T = int64_t> T modpow(T N, T P, T M) { T ret{1}; N %= M; while (P) { if (P & 0x01) { ret *= N; ret %= M; } P >>= 1; N *= N; N %= M; } return ret; }

/** code for assert debug begin */
int gErr = 0;
#define ASSERT(p) if(!(p)){ gErr = 1; }else{ ; }
/** code for assert debug end */

struct Tmp
{
public:
  int N;
  Tmp(int N)
  : N(N)
  {}
};

void solve(void)
{
  int N; cin >> N;
  vector<int> A(N);
  for (auto& a : A) { cin >> a; }
  set<int> s{A.begin(), A.end()};

  vector<int> mp(100001);
  for (const auto& a : A) {
    ++mp[a];
  }
  int max = s.size();

  ll stack = 0;
  for (int n = 1; n <= 100000; ++n) {
    if (mp[n] < 2) {
      continue;
    }
    if (mp[n] % 2 == 0) {
      mp[n] = 1;
      if (stack) {
        --stack;
      } else {
        ++stack;
      }
    } else {
      mp[n] = 1;
    }
  }
  if (stack) {
    max -= stack;
  }
  cout << max << CRLF;
  return;
}

int main(void)
{
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(0);

  solve();

  return 0;
}