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: Accepted)

import java.util.*;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] a = new long[n];
		int minus = 0;
		int zero = 0;
		long[] absmin = new long[2];
		Arrays.fill(absmin,Integer.MAX_VALUE);
		for(int i = 0;i<n;i++){
			a[i] = sc.nextLong();
			if(a[i]<0)minus++;
			if(a[i]==0)zero++;
			if(Math.abs(a[i])<absmin[1]){
				absmin[1]=Math.abs(a[i]);
				absmin[0]=i;
			}
		}
		sc.close();
		long ans = 0;
		if(zero!=0 || minus%2==0){
			for(int i = 0;i<n;i++){
				ans += (long)Math.abs(a[i]);
			}
		}else{
			for(int i = 0;i<n;i++){
				if(i!=absmin[0])ans += (long)Math.abs(a[i]);
			}
          ans-=absmin[1];
		}
		System.out.println(ans);
	}
}