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 Kotlin (1.3.71) (judge verdict: Wrong Answer)

import java.io.PrintWriter
import kotlin.math.max

fun main() {
    PrintWriter(System.out).use { out ->
        solve(out)
        out.flush()
    }
}

fun solve(out: PrintWriter) {
    val n = readInteger()
    val aList = readLongList()

    val tmp1 = aList.filterIndexed { index, _ -> index % 2 == 0 }
    val tmp2 = aList.filterIndexed { index, _ -> index % 2 == 1 }

    val sum1 = tmp1.sum()
    val sum2 = tmp2.sum()
    if (n % 2 == 0) {
        println(max(sum1, sum2))
    } else {
        var aa = calcCumulativeSumList(tmp1)
        var bb = calcCumulativeSumList(tmp2)

//        println(aa)
//        println(bb)

        var ans = Long.MIN_VALUE
        for (i in 0 until aa.size) {
            val aa1 = if (i < aa.size && i < bb.size) aa[i] + sum2 - bb[i] else Long.MIN_VALUE
            ans = max(ans, aa1)
        }
        ans = max(ans, aa[aa.size - 2])

        for (i in 0 until bb.size) {
            val aa2 = if (i + 1 < aa.size && i < bb.size) bb[i] + sum1 - aa[i + 1] else Long.MIN_VALUE
            ans = max(ans, aa2)
        }
        ans = max(ans, bb[bb.size - 1])

        println(ans)
    }
}

fun calcCumulativeSumList(list: List<Long>) = list.fold(mutableListOf(0L)) { acc, value ->
    acc += acc.last() + value
    acc
}

fun readInteger() = readLine()!!.toInt()
fun readLong() = readLine()!!.toLong()
fun readStringList() = readLine()!!.split(" ")
fun readIntegerList() = readStringList().map(String::toInt)
fun readLongList() = readStringList().map(String::toLong)
fun readDoubleList() = readStringList().map(String::toDouble)