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: Runtime Error)

import java.util.Scanner;

public class Main {

	private static long[] A;

	public static void main(String[] args) {
		//Input
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());

		long[] A = new long[N];
		for(int i = 0 ; i < N ; i++ ) {
			A[i] = Integer.parseInt(sc.next());
		}

		//Logic
		long answer = dp(N, 0);

		//Output
		System.out.println(answer);

	}

	private static long dp(int i, int j) {
		if(i == 0 && j == 0) {
			return 0;
		} else if (i == 0 && j == 1) {
			return -1000000000;
		}

		if(j == 0) {
			return Math.max(dp(i-1,0)+A[i-1], dp(i-1,1)-A[i-1]);
		} else {
			return Math.max(dp(i-1,0)-A[i-1], dp(i-1,1)+A[i-1]);
		}

	}

}