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 Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defparameter *a* #())
(defparameter *ans* 0)

(defun solve ()
  (loop :for i :across *a*
        :do (setf *ans* (+ *ans* (abs i))))

  (if (oddp (loop :for i :across *a* :count (<= i 0)))
      (let ((minimum 1000000000000))
        (loop :for i :across *a* :do (setf minimum (min minimum (abs i))))
        (setf *ans* (- *ans* (abs minimum)))))
  *ans*)

(defun main ()
  (let* ((n (read))
         (a (loop :repeat n :collect (read))))
    (setf *a* (make-array (length a) :initial-contents a))
    (format t "~A~%" (solve))))

(main)