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: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int gcd(int a, int b) {
	if (b == 0)
		return a;
	else {
		int x = a % b;
		a = b;
		b = x;
		gcd(a, b);
	}
}

int ch(int a, int b) {
	if (a < b)
		swap(a, b);
	return gcd(a, b);
}

int main() {
	int n;
	cin >> n;
	vector<int> da(n),fo(n),ba(n);
	for (int i = 0;i < n;i++)
		cin >> da[i];

	if (n == 2) {
		cout << max(da[0], da[1]) << endl;
		return 0;
	}
	int x = da[0];
	fo[0] = x;
	for (int i = 1;i < n;i++) {
		fo[i] = ch(fo[i-1], da[i]);
	}
	x = da[n - 1];
	ba[n - 1] = x;
	for (int i = n - 2;i > -1;i--) {
		ba[i] = ch(ba[i+1], da[i]);
	}
	int ans = max(ba[1],fo[n-2]);
	for (int i = 1;i < n - 1;i++)
		ans = max(ans, ch(fo[i - 1], ba[i + 1]));
	cout << ans << endl;
}