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.chomp.to_i
a= gets.chomp.split.map(&:to_i)
cnt = 0
n.times { |i|
  if a[i] < 0
    cnt += 1
  end
}
sum = 0
if cnt % 2 == 0
  n.times { |i|
    sum += a[i].abs
  }
else
  min = a[0]
  n.times { |i|
    if min > a[i]
      min = a[i].abs
    end
  }
  n.times { |i|
    sum += a[i].abs
  }
  sum -= 2*min.abs
end
puts sum
# while true
#   cnt = 0
#   (0..n-2).each{ |i|
#     if a[i] + a[i + 1] < 0
#       cnt += 1
#       a[i] = -a[i]
#       a[i + 1] = -a[i + 1]
#     end
#   }
#   if cnt == 0
#     puts a.sum
#     exit
#   end
# end