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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

var a:array[1..100010]of integer;
    n,i,j,m,mabs:integer;
    ans:int64;
    zero:boolean;
begin
  readln(n);
  m:=0;
  zero:=false;
  mabs:=100000010;
  for i:=1 to n do begin
    read(a[i]);
    if mabs>abs(a[i]) then 
      mabs:=abs(a[i]);
    if a[i]<0 then inc(m);
    if a[i]=0 then zero:=true
  end;
  ans:=0;
  for i:=1 to n do 
    if a[i]>0 then inc(ans,a[i])
    else inc(ans,-a[i]);
  if (m mod 2<>0) and not zero then
    ans:=ans-2*mabs;
  write(ans)
end.