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: Wrong Answer)

use std::io::Read;
use std::str::SplitWhitespace;
use std::str::FromStr;

pub fn read_stdin() -> String {
    let mut s = String::new();
    ::std::io::stdin().read_to_string(&mut s).unwrap();
    s
}

pub trait Parse<T> {
    fn parse(&mut self) -> T;
}

impl<'a, T> Parse<T> for SplitWhitespace<'a>
where
    T: FromStr,
{
    fn parse(&mut self) -> T {
        let word = self.next().unwrap();
        word.parse().ok().unwrap()
    }
}

fn main() {
    let source = read_stdin();
    let mut iter = source.split_whitespace();
    let n = iter.parse();
    let v: Vec<i64> = (0..n).map(|_| iter.parse()).collect();
    let c = v.iter().filter(|&x| *x < 0_i64).count();
    let sum: i64 = v.iter().map(|x| x.abs()).sum();

    println!(
        "{}",
        if c % 2 == 0 {
            sum
        } else {
            sum - 2 * v.last().unwrap().abs()
        }
    );
}