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::cmp;
use std::cmp::max;
use std::cmp::min;
use std::collections::HashMap;
use std::collections::HashSet;
use std::fmt;
use std::io::stdin;
use std::io::Error;
use std::io::ErrorKind;
use std::io::Read;

#[derive(Debug)]
struct Input {
    n: usize,
    a: Vec<i64>,
}

fn handle_input(input_str: String) -> Result<Input, Error> {
    let mut iter = input_str.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();
    let mut a = Vec::new();
    for _ in 0..n {
        let v: i64 = iter.next().unwrap().parse().unwrap();
        a.push(v)
    }
    let input = Input { n: n, a: a };
    Ok(input)
}

fn gcd(a: u32, b: u32) -> u32 {
    if a == 0 {
        return b;
    }
    gcd(b % a, a)
}

fn handle_output(input: Input) -> Result<String, Error> {
    let mut b_not_flipped = input.a[0];
    let mut b_flipped = -input.a[0];
    for i in 1..input.n - 1 {
        let tmp = max(b_not_flipped + input.a[i], b_flipped - input.a[i]);
        b_flipped = max(b_not_flipped - input.a[i], b_flipped + input.a[i]);
        b_not_flipped = tmp;
    }
    let last = input.a.last().unwrap();
    Ok(format!("{}", max(b_not_flipped + last, b_flipped - last)))
}

fn main() {
    let mut input_str = String::new();
    let stdin = stdin();
    stdin.lock().read_to_string(&mut input_str).unwrap();
    let input = handle_input(input_str).unwrap();
    let output = handle_output(input).unwrap();
    println!("{}", output);
}