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)

N = gets.to_i
A = gets.split(' ').map{|x| x.to_i}
s = 0
for x in A
  s = s + x.abs
end

l = Array.new(N)
r = Array.new(N)

l[0] = false
for i in 0...N-1
  l[i+1] = (A[i] < 0 && !l[i]) || (A[i] > 0 && l[i])? true : false
end

r[N-1] = false
for j in 0...N-1
  i = N - j - 1
  r[i-1] = (A[i] < 0 && !r[i]) || (A[i] > 0 && r[i])? true : false
end

ans = -10000000000000000000
for i in 0...N
  f = l[i] != r[i]? true : false
  if (A[i] < 0 && f == true) || (A[i] > 0 && f == false)
    ans = s
  else
    ans = [ans, s - 2 * A[i].abs].max
  end
end

p ans