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>
using namespace std;



int main() {
	
	int n;
	long long a[100001];
	long long b[100001];
	int num = 0;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
		
	}
	for (int i = 0; i < n; i++) {
		if (a[i] >= 0) {
			b[i] = a[i];
		}
		else {
			num++;
			b[i] = -1 * a[i];
		}
	}
	
	
	long long sum = 0;
	for (int i = 0; i < n; i++) {
		sum += b[i];
	}
	if (num % 2 == 0) cout << sum;
	else {
		long long  min = 1000000001;

		for (int i = 0; i < n; i++) {
			if (b[i] < min) min = b[i];
		}
		sum = sum - 2 * min;
		cout << sum;
	}
	
	return 0;
}