100533: [AtCoder]ABC053 D - Card Eater

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

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

Input

题意翻译

有一堆牌,每张牌上有一个数字。 每次可以取出其中3张,丢掉数字最大的和数字最小的牌,把中间那张再放回牌堆。 要求最后所有剩余牌上的数字互不相同,求最多能剩几张牌。

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