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)

//
//  respect the past, embrace the future
//  flipping signs
//

#include  <algorithm>
#include  <iostream>
#include  <climits>
#include  <cstdlib>
#include  <cstring>
#include  <cmath>
#include  <cstdio>
#include  <unordered_map>
#include  <map>
#include  <set>
#include  <stack>
#include  <string>
#include  <vector>
#include  <queue>

using namespace :: std;

using vpll = vector <pair <long long, long long> >;
using pll = pair <long long, long long>;
using vll = vector <long long>;
using ll = long long;

#define N (long long) (2e6 + 7)
#define M (long long) (1e9 + 7)
#define INF (long long) (2e18)
#define F first
#define S second

inline void fastInputOutput () {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL); cout.tie(NULL);
}

inline void ReadWriteFromFile () {
  freopen("../in.txt", "r", stdin);
  freopen("../out.txt", "w", stdout);
}

ll n, ans, a[N], mn = INF, cnt, neg;

int32_t main (int argc, char *argv[]) {
  fastInputOutput();
  // ReadWriteFromFile();
  
  cin >> n;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    neg += (a[i] < 0);
    cnt += (!a[i]);
    ans += abs(a[i]);
    mn = min(mn, abs(a[i]));
  }
  if (!cnt && (neg & 1))
    ans -= mn * 2;
  cout << ans;
}