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<iostream>
#include<vector>
#include <algorithm>

int main()
{
	int N;
	std::vector<int> As;

	std::cin >> N;

	int num_minus = 0;
	for (int i = 0; i < N; ++i) {
		int A;
		std::cin >> A;
		As.push_back(A);

		if (A < 0) {
			++num_minus;
		}
	}
	long sum = 0;
	if (num_minus % 2 == 0) {
		for (int i = 0; i < N; ++i) {
			sum += std::abs(As[i]);
		}
	}
	else {
		std::vector<int> As_abs;
		for (int i = 0; i < N; ++i) {
			const int A_abs = std::abs(As[i]);
			sum += A_abs;
			As_abs.push_back(A_abs);
		}

		int min = *std::min_element(As_abs.begin(), As_abs.end());
		sum -= 2 * min;
	}
	std::cout << sum;

	return 0;
}