Problem:
Score : 300 points

Problem Statement

You are given an integer sequence of length N. The i-th term in the sequence is a_i.
In one operation, you can select a term and either increment or decrement it by one.

At least how many operations are necessary to satisfy the following conditions?

For every i (1≤i≤n), the sum of the terms from the 1-st through i-th term is not zero.

For every i (1≤i≤n-1), the sign of the sum of the terms from the 1-st through i-th term, is different from the sign of the sum of the terms from the 1-st through (i+1)-th term.

Constraints

2 ≤ n ≤ 10^5

|a_i| ≤ 10^9

Each a_i is an integer.

Input

Input is given from Standard Input in the following format:

n
a_1 a_2 ... a_n

Output

Print the minimum necessary count of operations.

Sample Input 1

4
1 -3 1 0

Sample Output 1

4

For example, the given sequence can be transformed into 1, -2, 2, -2 by four operations. The sums of the first one, two, three and four terms are 1, -1, 1 and -1, respectively, which satisfy the conditions.

Sample Input 2

5
3 -6 4 -5 7

Sample Output 2

0

The given sequence already satisfies the conditions.

Sample Input 3

6
-1 4 3 2 -5 4

Sample Output 3

8

Solution in Rust (1.15.1) (judge verdict: Accepted)

#![allow(unused_imports, unused_macros, dead_code)]

macro_rules! min {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| min!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = min!($($ys),*);
        if $x < t { $x } else { t }
    }}
}
macro_rules! max {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        it.next().map(|z| it.fold(z, |x, y| max!(x, y)))
    }};
    ($x:expr) => ($x);
    ($x:expr, $($ys:expr),*) => {{
        let t = max!($($ys),*);
        if $x > t { $x } else { t }
    }}
}
macro_rules! ewriteln {
    ($($args:expr),*) => { let _ = writeln!(&mut std::io::stderr(), $($args),*); };
}
macro_rules! trace {
    ($x:expr) => { ewriteln!(">>> {} = {:?}", stringify!($x), $x) };
    ($($xs:expr),*) => { trace!(($($xs),*)) }
}
macro_rules! put {
    (.. $x:expr) => {{
        let mut it = $x.iter();
        if let Some(x) = it.next() { print!("{}", x); }
        for x in it { print!(" {}", x); }
        println!("");
    }};
    ($x:expr) => { println!("{}", $x) };
    ($x:expr, $($xs:expr),*) => { print!("{} ", $x); put!($($xs),*) }
}

const M: i64 = 1_000_000_007;

trait Group: std::ops::Add<Output=Self> + std::ops::Sub<Output=Self> + std::ops::Neg<Output=Self>
    + std::iter::Sum + Clone + Copy {
    fn zero() -> Self;
}
impl Group for i32 { fn zero() -> Self { 0 }}
impl Group for i64 { fn zero() -> Self { 0 }}
impl Group for f32 { fn zero() -> Self { 0.0 }}
impl Group for f64 { fn zero() -> Self { 0.0 }}

trait Ring: Group + std::ops::Mul<Output=Self> + std::ops::Div<Output=Self> {
    fn one() -> Self;
}
impl Ring for i32 { fn one() -> Self { 1 }}
impl Ring for i64 { fn one() -> Self { 1 }}
impl Ring for f32 { fn one() -> Self { 1.0 }}
impl Ring for f64 { fn one() -> Self { 1.0 }}

#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Copy, Debug)]
enum Hyper<X> { NegInf, Real(X), Inf }
use Hyper::{Real, NegInf, Inf};
impl<X> Hyper<X> {
    fn unwrap(self) -> X { if let Hyper::Real(x) = self { x } else { panic!() } }
}
impl<X: Ring> std::ops::Add for Hyper<X> {
    type Output = Self;
    fn add(self, rhs: Hyper<X>) -> Hyper<X> {
        match (self, rhs) {
            (Real(x), Real(y)) => Real(x + y),
            (Inf, _) => Inf,
            (_, Inf) => Inf,
            _ => NegInf,
        }
    }
}
impl<X: Ring> std::ops::Sub for Hyper<X> {
    type Output = Self;
    fn sub(self, rhs: Hyper<X>) -> Hyper<X> { self + (-rhs) }
}
impl<X: Ring> std::ops::Neg for Hyper<X> {
    type Output = Self;
    fn neg(self) -> Hyper<X> {
        match self {
            Inf => NegInf,
            NegInf => Inf,
            Real(x) => Real(-x),
        }
    }
}

fn solve(d: i64, sign: bool, xs: &Vec<i64>) -> i64 {
    let mut sign = sign;
    let mut sum = 0;
    let mut num = 0;
    for &x in xs.iter() {
        sum += x;
        if sign {
            if sum < 1 {
                num += 1 - sum;
                sum = 1;
            }
            else if sum > d {
                num += sum - d;
                sum = d;
            }
            sign = false;
        } else {
            if sum > -1 {
                num += sum + 1;
                sum = -1;
            }
            else if sum < -d {
                num += -d - sum;
                sum = -d;
            }
            sign = true;
        }
    }
    num
}

fn main() {
    let mut sc = Scanner::new();
    let n: usize = sc.cin();
    let xs: Vec<i64> = sc.vec(n);

    let d = 1000000003;
    put!(min!(solve(d, true, &xs), solve(d, false, &xs)));

}

use std::io::{self, Write};
use std::str::FromStr;
use std::collections::VecDeque;

struct Scanner { stdin: io::Stdin, buffer: VecDeque<String>, }
impl Scanner {
    fn new() -> Self { Scanner { stdin: io::stdin(), buffer: VecDeque::new() } }
    fn cin<T: FromStr>(&mut self) -> T {
        while self.buffer.len() == 0 {
            let mut line = String::new();
            let _ = self.stdin.read_line(&mut line);
            for w in line.split_whitespace() {
                self.buffer.push_back(String::from(w));
            }
        }
        self.buffer.pop_front().unwrap().parse::<T>().ok().unwrap()
    }
    fn chars(&mut self) -> Vec<char> { self.cin::<String>().chars().collect() }
    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T> { (0..n).map(|_| self.cin()).collect() }
}