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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

typedef long long int lli;
typedef unsigned long long int ulli;
typedef pair<int,int> pii;
typedef priority_queue< int, vector< int >, greater< int > >  minHeap;

#define ones(x) __builtin_popcount(x)
#define onesl(x) __builtin_popcountl(x)
#define onesll(x) __builtin_popcountll(x)

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define scn(n) scanf("%d",&n)
#define scnll(n) scanf("%lld",&n)
#define scn2(n,m) scanf("%d%d",&n,&m)
#define scn3(n,m,w) scanf("%d%d%d",&n,&m,&w)
#define scn2ll(n,m) scanf("%lld%lld",&n,&m)
#define atoz(v) v.begin(),v.end()
#define ratoz(v) v.rbegin(),v.rend()
#define Fill(a,v) memset(a,v,sizeof(a))
#define sz(v) v.size()
#define fi first
#define se second
#define inf 1e9
#define pi acos(-1.0)
#define sqr(x) x*x
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))
#define ten(n) (int)1e##n
#define tenll(n) (lli)1e##n
#define mod 1000000007
#define FastIO ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);

int Set(int N,int pos)
{
    return N=N | (1<<pos);
}
int reset(int N,int pos)
{
    return N = N & ~(1<<pos);
}
bool check(int N,int pos)
{
    return (bool)(N & (1<<pos));
}


inline int addmod(int x ,int y){return (x%mod + y%mod)%mod;}
inline int submod(int x ,int y){return (x%mod - y%mod + mod)%mod;}
inline int mulmod(int x ,int y){return (x%mod *1LL* y%mod)%mod;}
inline int nextSubMask(int i , int mask) {return (i-1)&mask;} /// returns next smallest submask

void we_r_done(){cout<<"NO"; exit(0);}

void debug(bool ok , string mssg)
{
    if(ok)return;
    cout<<mssg;
    exit(0);
}

int main()
{
    ///freopen("output.txt","w",stdout);
    ///freopen("input.txt","r",stdin);

    FastIO;

    int n;
    cin>>n;

    int a[n];

    set<int>st;
    map<int,int>cnt;

    for(int i=0; i<n; i++){
        cin>>a[i];
        st.insert(a[i]);
        cnt[a[i]]++;
    }
    int more = 0 , mx = 0;

    for(auto it : cnt){

        if(it.se>1){
            if(it.se%2==0){
                more++;
                mx = max(mx , it.se);
            }
        }
    }
    int ans = st.size();
    if(more%2){
        if(mx==2 || (more==1 && mx%2==0)) ans--;
    }

    cout<<ans;

    return 0;

}

///sin and cos expect input in radians not degrees. so use , sin(degrees * pi / 180)
///using bs = bitset<MX>; // how many distinct number can be form?