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)

object Main {
  def main(args: Array[String]): Unit = {
    solve
  }

  def solve(): Unit = {
    val sc = new java.util.Scanner(System.in)
    val n = sc.nextInt()
    val as = new Array[Long](n)
    for (i <- 0 until n) {
      as(i) = sc.nextLong()
    }

    if (as.count(_ < 0) % 2 == 0) {
      // 負の数の個数が偶数の場合、すべての負の符号を反転できる
      val ans = as.foldLeft(0L)((z, v) => z + math.abs(v))
      println(ans)
    } else {
      // 負の数の個数が奇数個の場合、負の数を1つ残して残りの符号を反転できる
      // 残すのは絶対値が最小の数
      val remainedNum = as.foldLeft(Long.MaxValue)((z, v) => if (z > math.abs(v)) math.abs(v) else z)

      // すべての値の絶対値を合算したものから、残った負の数の絶対値 * 2を引く
      val ans = as.foldLeft(0L)((z, v) => z + math.abs(v)) - 2 * remainedNum
      println(ans)
    }
  }
}