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 FOR(i,a,b) for(int i=(a);i<=(b);++i) 
#define RFOR(i,a,b) for(int i=(a);i>=(b);--i) 
#define REP(i,n) for(int i=0;i<(n);++i)
#define RREP(i,n) for(int i=(n);i>0;--i)
#define CI cin>> 
#define CO cout<<
#define EN <<endl 
#define all(x) (x).begin(),(x).end()
using namespace std;
template <typename T> istream& operator >> (istream& is, vector<T>& vec) { for (T& x : vec) is >> x; 	return is; }
using ll = long long;
using VI = vector<int>;

int main() {
	ll count = 0, ans = 0;
	int n; CI n;
	vector<long long> v(n); CI v;
	REP(i, n) {
		if (v[i] < 0) {
			v[i] = v[i] * -1;
			count++;
		}
		ans += v[i];
	}
	sort(all(v));
	if (count % 2) {
		ans -= v[0]*2;
	}
	CO ans EN;
}