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.*;
import java.io.*;
 
public class Main {
  static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
  static PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
  
  public static void main(String[] args) throws Exception {
    int n = Integer.parseInt(br.readLine());
    String[] split = br.readLine().split(" ");
    long[] arr = new long[n];
    
    for(int i = 0; i < n; i++) {
      arr[i] = Long.parseLong(split[i]);
    }
    long sum = 0;
    long min = Long.MAX_VALUE;
    int negs = 0;
    for(long i : arr) {
      if(i < 0)
        negs++;
      long abs = Math.abs(i);
      min = Math.min(min, abs);
      sum += abs;
    }
    if(negs % 2 == 1)
        sum -= min * 2;
    
    pw.println(sum);
    
    pw.close();
  }
}