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>

#define REP(i, n) for(decltype(n) i = 0; i < n; i++)

#define ALL(c)   c.begin(), c.end()
#define SORT(c)  std::sort(ALL(c))
#define RSORT(c) std::sort(ALL(c), std::greater<decltype(c)::value_type>())

using namespace std;
using ll = long long;

const int MOD  = (int)1e9 + 7;
const int INF  = (int)1e9 + 1;
const ll  LINF = (ll)1e18 + 1;

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    std::cin >> N;

    int  minus_cnt            = 0;
    bool exist_zero           = false;
    int  min_val_without_zero = INF;
    vector<int> A(N);
    REP(i, N) {
        std::cin >> A[i];
        if(A[i] < 0) minus_cnt++;
        if(A[i] == 0) exist_zero = true;
        A[i] = abs(A[i]);
        if(A[i] != 0) min_val_without_zero = min(min_val_without_zero, A[i]);
    }

    if(exist_zero || minus_cnt % 2 == 0) {
        std::cout << accumulate(ALL(A), 0LL) << std::endl;
    }
    else {
        std::cout << accumulate(ALL(A), 0LL) - min_val_without_zero * 2 << std::endl;
    }

    return 0;
}