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 Rust (1.15.1) (judge verdict: Accepted)

use std::vec::Vec;
use std::cmp;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}


fn abs(x: i64) -> i64 {
    if x < 0  {
        return -x;
    } else {
        return x;
    }
}

fn main() {
    let n: usize = read();
    let mut a: Vec<i64> = read_vec();

    // solve1(n, &a);
    solve2(n, &mut a);
}

fn solve1(n: usize, v: &Vec<i64>) {
  let mut minus: u64 = 0;

  for i in 0..n {
      if v[i] < 0 {
          minus += 1;
      }
  }
  let mut ans: i64 = 0;

  if minus % 2 == 0 {
      for i in 0..n {
          ans += abs(v[i]);
      }
  } else {
      let mut minabs = 10000000000;
      for i in 0..n {
          if abs(v[i]) < minabs {
              minabs = abs(v[i]);
          }
          ans += abs(v[i]);
      }
      ans += -2*minabs;
  }
  println!("{}", ans);
}


fn solve2(n: usize, v: &mut Vec<i64>) {
  let mut dp: Vec<Vec<i64>> = [vec![0; n], vec![0; n]].to_vec();
  dp[0][0] = v[0];
  dp[1][0] = std::i64::MIN/2;
  for i in 1..n {
    dp[0][i] = cmp::max(dp[0][i-1], dp[1][i-1]) + v[i];
    dp[1][i] = cmp::max(dp[0][i-1] - 2*v[i-1], dp[1][i-1] + 2*v[i-1]) - v[i];
  }

  println!("{:?}", cmp::max(dp[0][n-1], dp[1][n-1]));
}