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 Python (3.4.3) (judge verdict: Accepted)

# import sys  sys.exit()を使う時に必要

def main():
  if 'get_ipython' not in globals():  
    # For Subsession
    N = int(input())
    # A, B, C = input().split()
    A = [int(i) for i in input().split()] 
    # S = [input() for _ in range(N)]  縦持ち／行数N
    # t = [0] * N  　　ti xi yi 縦持ち/行数N
    # x = [0] * N
    # y = [0] * N
    # for i in range(N):
    #   t[i], x[i], y[i] = map(int, input().split())
  else:
    #A = [-10,5,-4]
    #A = [10,-4,-8,-11,3]
    A = [-1000000000,1000000000,-1000000000,1000000000,-1000000000,0,1000000000,-1000000000,1000000000,-1000000000,1000000000]
    N = len(A)

  # Processing
  # if 'get_ipython' in globals(): print("debug")
  sumA = 0
  min_abs = 1000000000
  cnt_minus = 0
  for a in A:
    if a < 0 :
      cnt_minus +=1
    if abs(a) < min_abs: 
      min_abs = abs(a)
    sumA += abs(a)
  
  if cnt_minus % 2 > 0:
    sumA -= min_abs * 2
  
  print(sumA)

main()