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)

fun main(arg: Array<String>) {
    val N = nextInt()
    val A = listOfLong()
    val evenA = LongArray(N)
    val oddA = LongArray(N)
    A.forEachIndexed { index, a ->
        if (index % 2 == 0) evenA[index] = a
        else oddA[index] = a
    }
    for (n in 1 until N) {
        evenA[n] += evenA[n - 1]
        oddA[n] += oddA[n - 1]
    }
    if (N % 2 == 0) { //even
        val ans = Math.max(evenA.last(), oddA.last())
        return println(ans)
    }
    //odd
    var ans = evenA.last()
    for (n in 0 until N step 2)
        ans = Math.max(ans, evenA.last() - A[n])
    for (n in 0 until N - 3 step 2)
        ans = Math.max(ans, evenA[n] + (oddA.last() - oddA[n + 3]))
    for (n in 1 until N - 2 step 2)
        ans = Math.max(ans, oddA[n] + (evenA.last() - evenA[n + 3]))

    return println(ans)
}

fun next() = readLine()!!
fun nextInt(offset: Int = 0) = Integer.parseInt(next()) + offset
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun listOfString() = next().split(" ")
fun listOfInt() = listOfString().map(String::toInt)
fun listOfLong() = listOfString().map(String::toLong)
fun listOfDouble() = listOfString().map(String::toDouble)
fun listOfInt(offset: Int = 0) = listOfString().map { Integer.parseInt(it) + offset }
fun listOfInt(vararg offset: Int) = listOfString().map { Integer.parseInt(it) }.mapIndexed { index, int -> int + offset[index % offset.size] }
fun listOfLong(offset: Long = 0L) = listOfString().map { java.lang.Long.parseLong(it) + offset }
fun listOfLong(vararg offset: Long) = listOfString().map { java.lang.Long.parseLong(it) }.mapIndexed { index, long -> long + offset[index % offset.size] }