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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
#define lli long long int
#define rep(i, n) ;for (int i = 0;i < (int)(n);i++)
#define rep2(i, s, n) ;for (int i = s; i < (int)(n);i++)
#define ALL(vec)  (vec).begin(),(vec).end()
#define pi 3.1415926535897932384626433832795
#define MAX_INF 9223372036854775807
#define MIN_INF (922337203685477587+1)
#define sosuu 1000000007


int main()
{
  int N;
  lli ans=0,hold,mi=922337203685477587;
  int in=0;
  cin >> N;
  rep(i, N){
  cin >> hold;
    if(hold<0){
      hold*=-1;
      in++;
    }
    mi = min(mi,hold);
    ans+=hold;
  }
  if(in%2==0){
  cout << ans << endl;
  }  
  else {
  cout << ans-2*mi<< endl;
  }
}