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)

#pragma GCC optimize("O2,Ofast,inline,unroll-all-loops,-ffast-math")
#include <bits/stdc++.h>
#define pb(X) push_back(X)
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
using namespace std;

int n, a, b, c, d, q, ans;

int main() {
	INIT
	cin >> n;
	vector<long long > A(n);
	long long ans = 0;
	for (int i = 0; i < n; ++i) cin >> A[i];
	for (int i = 0; i < n - 2; ++i) {
		if (A[i] < 0) {
			A[i] = -A[i];
			A[i + 1] = -A[i + 1];
		}
		ans += A[i];
	}
	if (A[n - 2]  > 0 && A[n - 1] > 0) {
		ans += A[n - 2] + A[n - 1];
	} else if (A[n - 2] < 0 && A[n - 1] < 0) {
		ans += -A[n - 2] + -A[n - 1];
	} else {
		ans += max(abs(A[n - 2]), abs(A[n - 1])) - min(abs(A[n - 2]), abs(A[n - 1]));
	}
	//puts("");
	//for (int i = 0; i < n; ++i) cout << A[i] << ' ';
	cout << ans;
	return 0;
}