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)

use std::io::stdin;
use std::str::FromStr;
use std::cmp::min;

fn main(){
    let _: usize = get_one();
    let xs: Vec<i64> = get_vec();

    let ans1 = solve(&xs);
    let ans2 = solve(&(xs.iter().map(|&x| -x).collect()));

    println!("{}", min(ans1, ans2));
}

fn solve(xs: &Vec<i64>) -> i64 {
    let mut acc = 0;
    let mut ans = 0;

    for i in 0..xs.len() {
        acc += xs[i];
        if acc * (1 - 2*(i%2) as i64) <= 0 {
            ans += (1 - 2*(i%2) as i64 - acc).abs();
            acc = 1 - 2*(i%2) as i64;
        }
    }

    ans
}

#[allow(dead_code)]
fn get_line() -> String {
    let mut s = String::new();
    match stdin().read_line(&mut s){
        Ok(_) => {s.trim().to_string()}
        Err(_) => String::new()
    }
}

#[allow(dead_code)]
fn get_vec<T: std::str::FromStr>() -> Vec<T> {
    let line = get_line();
    line.split_whitespace().filter_map(|x| x.parse().ok()).collect()
}

#[allow(dead_code)]
fn get_one<T: FromStr + Copy>() -> T {
    let v = get_vec();
    v[0]
}

#[allow(dead_code)]
fn get_pair<T: FromStr + Copy>() -> (T, T) {
    let v = get_vec();
    (v[0], v[1])
}

#[allow(dead_code)]
fn get_triple<T: FromStr + Copy>() -> (T, T, T) {
    let v = get_vec();
    (v[0], v[1], v[2])
}

#[allow(dead_code)]
fn get_chars() -> Vec<char> {
    get_line().chars().collect()
}