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.Scanner;

public class Main {
    void run() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long sum = 0;
        long min = Long.MAX_VALUE;
        int count = 0;
        for (int i = 0; i < n; i++) {
            long a = sc.nextLong();
            sum += Math.abs(a);
            min = Math.min(min, Math.abs(a));
            if (a < 0) {
                count++;
            }
        }
        if (count % 2 == 0) {
            System.out.println(sum);
        } else {
            System.out.println(sum - 2 * min);
        }
    }

    void run2() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] as = new long[n];
        for (int i = 0; i < n; i++) {
            as[i] = sc.nextLong();
        }
        long[][] dp = new long[n][2];
        dp[0][0] = as[0];
        dp[0][1] = -as[0];
        for (int i = 1; i < n; i++) {
            dp[i][0] = Math.max(dp[i - 1][0] + as[i], dp[i - 1][1] - as[i]);
            dp[i][1] = Math.max(dp[i - 1][0] - as[i], dp[i - 1][1] + as[i]);
        }
        System.out.println(dp[n - 1][0]);
    }

    public static void main(String[] args) {
        new Main().run2();
    }
}