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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.lang.*;
import java.io.*;

public class Main{
public static void main (String[] args){
	Scanner sc = new Scanner(System.in);
	int  n = Integer.parseInt(sc.next());
	long Pmin = 0; long Nmin = 0;
	long Psum = 0; long Nsum = 0;
	boolean flag = false;
	List<Long> positive = new ArrayList<Long>();
	List<Long> negative = new ArrayList<Long>();
	for(int i = 0; i < n; i++){
		long a = Long.parseLong(sc.next());
		if(a > 0){
			if(positive.isEmpty())Pmin = a;
			positive.add(a);
			Pmin = Math.min(Pmin,a);
			Psum += a;
		}else if(a < 0){
			long b = Math.abs(a);
			if(negative.isEmpty())Nmin = b;
			negative.add(b);
			Nmin = Math.min(Nmin,b);
			Nsum += b;
		}else{
			flag = true;
		}
	}
	if(negative.size()%2 == 0 || flag){
		System.out.println(Psum + Nsum);
	}else{
		System.out.println(Psum + Nsum - Math.min(Pmin,Nmin)*2);
	}
}
}