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.

Examples

Input

3
-10 5 -4


Output

19


Input

5
10 -4 -8 -11 3


Output

30


Input

11
-1000000000 1000000000 -1000000000 1000000000 -1000000000 0 1000000000 -1000000000 1000000000 -1000000000 1000000000


Output

10000000000
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Scanner;

public class Main {

  public static void main(String[] args) {
    resolve(System.in, System.out);
  }

  static void resolve(InputStream is, PrintStream pw) {
    Scanner sc = new Scanner(is);
    int n = Integer.parseInt(sc.next());
    long[] a = new long[n];
    for (int i = 0; i < n; i++) {
      a[i] = Long.parseLong(sc.next());
    }
    long[][] dp = new long[n + 1][2];
    dp[0][0] = 0;
    dp[0][1] = Integer.MIN_VALUE;

    for (int i = 0; i < n; i++) {
      dp[i + 1][0] = Math.max(dp[i][0] + a[i], dp[i][1] - a[i]);
      dp[i + 1][1] = Math.max(dp[i][0] - a[i], dp[i][1] + a[i]);
    }
    pw.println(dp[n][0]);
  }
}
