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)

pub fn main() {
    use std::io::Read;
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    
    let n: usize = iter.next().unwrap().parse().unwrap();
    let a: Vec<i64> = iter.take(n).map(|x| x.parse().unwrap()).collect();

    let mut minus_is_even: bool = true;
    for i in 0..n {
        if a[i] < 0 {
            minus_is_even = !minus_is_even;
        }
    }

    if minus_is_even {
        let sum = a.iter().map(|x| x.abs()).fold(0, |acc, x| acc + x);
        println!("{}", sum);
    } else {
        let mut abs_min_value: (i64, usize) = (std::i64::MAX, 0);
        for i in 0..n {
            if a[i].abs() < abs_min_value.0.abs() {
                abs_min_value = (a[i], i);
            }
        }
        let mut sum = 0;
        for i in 0..n {
            if i == abs_min_value.1 {continue;}
            sum += a[i].abs();
        }
        sum -= abs_min_value.0.abs();
        println!("{}", sum);
    }
}