Problem:
Score : 400 points

Problem Statement

There are N integers, A_1, A_2, ..., A_N, arranged in a row in this order.

You can perform the following operation on this integer sequence any number of times:

Operation: Choose an integer i satisfying 1 \leq i \leq N-1. Multiply both A_i and A_{i+1} by -1.

Let B_1, B_2, ..., B_N be the integer sequence after your operations.

Find the maximum possible value of B_1 + B_2 + ... + B_N.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

-10^9 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible value of B_1 + B_2 + ... + B_N.

Sample Input 1

3
-10 5 -4

Sample Output 1

19

If we perform the operation as follows:

Choose 1 as i, which changes the sequence to 10, -5, -4.

Choose 2 as i, which changes the sequence to 10, 5, 4.

we have B_1 = 10, B_2 = 5, B_3 = 4. The sum here, B_1 + B_2 + B_3 = 10 + 5 + 4 = 19, is the maximum possible result.

Sample Input 2

5
10 -4 -8 -11 3

Sample Output 2

30

Sample Input 3

11
-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000

Sample Output 3

10000000000

The output may not fit into a 32-bit integer type.

Solution in Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn

object Main {

  type State = Tuple3[Int, Int, Long]

  def update(state: State, num: Int): State = {
    val isMinus = if (num >= 0) 0 else 1
    val absNum = Math.abs(num)
    val sum = state._3 + (absNum: Long)

    Tuple3(state._1 + isMinus, if (state._2 >= absNum) absNum else state._2, sum)
  }

  def maxPossibleValue(state: State): Long = {
    if (state._1 % 2 == 0) state._3 else state._3 - (2 * state._2: Long)
  }

  def main(args: Array[String]): Unit = {
    val n = StdIn.readLine.toInt
    val as = StdIn.readLine.split(" ").map(_.toInt)

    println(maxPossibleValue(as.foldLeft((0, Int.MaxValue, 0): State)(update)))
  }
}