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 Ruby (2.3.3) (judge verdict: Wrong Answer)

N = gets.to_i
A = gets.chomp.split.map(&:to_i)

natural = []
minus = []
A.each do |a|
  if a < 0
    minus << a
  elsif
    natural << a
  end
end
natural.sort!
minus.sort!

if minus.length % 2 == 0
  ans = 0
  ans += natural.inject(:+) if natural.length > 0
  ans += minus.inject(:+) if minus.length > 0
  puts ans
else
  ans = 0
  if natural.length > 1
    natural[1..-1].each do |n|
      ans += n
    end
  end
  if minus.length > 1
    minus[0..-2].each do |m|
      ans -= m
    end
  end
  if natural.length > 0 and minus.length > 0 and natural[0] < -minus[-1]
    ans -= natural[0]
    ans -= minus[-1]
  else
    ans += natural[0] if natural.length > 0
    ans += minus[-1] if minus.length > 0
  end
  puts ans
end