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: Accepted)

nn = gets.to_i
aa = gets.split.map(&:to_i).sort

max = 0
idx = aa.bsearch_index{|x|x>=0}

if idx.nil?
  # 全部マイナス
  if nn%2==0
    # 全部プラスにできる
    max = -(aa.inject(:+))
  else
    # 1個だけマイナス残る
    b = aa.pop
    max = -(aa.inject(:+)) + b
  end
elsif idx==0
  # マイナスがない
  max = aa.inject(:+)
else
  # マイナスがある
  minus_cnt = idx
  if minus_cnt%2==0
    # 全部プラスにできる
    max = aa.inject{|s,i|s.abs+i.abs}
  else
    # 1こだけマイナス残る
    sorted = aa.sort_by{|a|a.abs}.to_a
    b = sorted.shift
    b=-b if b>0
    max = (sorted.inject{|s,i|s.abs+i.abs}).abs + b
  end
end

puts max