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;

using ll = long long;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<ll>>;

int main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  vll a(n);
  for (int i = 0; i < n; i++)
    cin >> a[i];
  sort(a.begin(), a.end());
  ll ans = 0;
  for (int i = 0; i < n; i++) {
    if (i == n - 1) {
      ans += a[i];
    } else if (a[i] <= 0 && a[i + 1] <= 0) {
      ans -= a[i] + a[i + 1];
      i++;
    } else if (a[i] <= 0 && a[i + 1] > 0) {
      ans += abs(a[i] + a[i + 1]);
      i++;
    } else {
      ans += a[i];
    }
  }
  cout << ans << endl;
  return 0;
}