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)

// Add compile option "-std=c++11" for C++11 compile.

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <regex>
#include <numeric>
using namespace std;

// Macro
#define rep(i, N) for(int i=0; i<(int)N; i++)

// Type
template <typename T> using P = pair<T, T>;
using ll = long long;
using ull = unsigned long long;

// Constants
const ll INF = 1e18;
const ll MOD = 1000000007;

int main() {
  int N;
  cin >> N;

  ll abs_sum = 0;   // 絶対値の総和
  ll abs_min = INF; // 絶対値の最小値
  int minus_n = 0;  // マイナス値の数
  bool zero_flag = false; // 0があるか
  rep(i, N) {
    ll A;
    cin >> A;

    if(A == 0) {
      zero_flag = true;
      continue;
    }

    if(A < 0) {
      minus_n++;
    }

    ll abs_A = abs(A);
    abs_sum += abs_A;
    abs_min = min(abs_min, abs_A);
  }

  if(zero_flag || minus_n % 2 == 0) {
    cout << abs_sum << endl;
  } else {
    cout << abs_sum - (2 * abs_min) << endl;
  }
}