Problem:
Score : 600 points

Problem Statement

Given is an integer sequence A_1, ..., A_N of length N.

We will choose exactly \left\lfloor \frac{N}{2} \right\rfloor elements from this sequence so that no two adjacent elements are chosen.

Find the maximum possible sum of the chosen elements.

Here \lfloor x \rfloor denotes the greatest integer not greater than x.

Constraints

2 \leq N \leq 2\times 10^5

|A_i|\leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the maximum possible sum of the chosen elements.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

12

Choosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.

Sample Input 2

5
-1000 -100 -10 0 10

Sample Output 2

0

Choosing -10 and 10 makes the sum 0, which is the maximum possible value.

Sample Input 3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Watch out for overflow.

Sample Input 4

27
18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49

Sample Output 4

295

Solution in Scala (2.13.1) (judge verdict: Accepted)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}
import scala.collection.mutable.{Map, Stack, Queue, PriorityQueue, Set}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  val N = in.next().toInt
  val A = new Array[Int](N+1)
  for (i <- 1 to N)
    A(i) = in.next().toInt

  //
  val dp = Array.ofDim[Long](N+1, 4)
  val init = Long.MinValue / 3
  for (i <- 0 to N; j <- 0 to 3)
    dp(i)(j) = init

  dp(0)(0) = 0
  for (i <- 0 until N; j <- 0 to 2) {
    if ((i+j) % 2 == 1) { // 使わない
      dp(i+1)(j) = Math.max(dp(i+1)(j), dp(i)(j))
    }
    else {
      dp(i+1)(j+1) = Math.max(dp(i+1)(j+1), dp(i)(j))
      dp(i+1)(j) = Math.max(dp(i+1)(j), dp(i)(j) + A(i+1))
    }
  }

  if (N % 2 == 0)
    println(Math.max(dp(N)(1), dp(N)(0)))
  else
    println(Math.max(dp(N)(2), dp(N)(1)))
}

object Sub {
  def print2DimArray[A](mat: Array[Array[A]]): Unit = {
    mat.foreach(lin => println(lin.toList))
  }
}

class InputReader(stream: InputStream) {
  private[this] val reader = new BufferedReader(new InputStreamReader(stream))
  private[this] var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}