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)

fn read() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).ok();
    buf.trim().to_string()
}

fn main() {
    let n: usize = read().parse().unwrap();
    let a: Vec<i64> = read()
        .split_whitespace()
        .map(|x| x.parse().unwrap())
        .collect();

    let mut sum = (0, 0);
    let mut cnt = (0, 0);
    use std::cmp::{max, min};
    for i in 0..n {
        sum.0 += a[i];
        sum.1 += a[i];
        let f = if i % 2 == 0 { (1, -1) } else { (-1, 1) };

        cnt.0 += max(0, 1 - sum.0 * f.0);
        sum.0 = max(1, sum.0 * f.0) * f.0;
        cnt.1 += max(0, 1 - sum.1 * f.1);
        sum.1 = max(1, sum.1 * f.1) * f.1;
    }
    println!("{}", min(cnt.0, cnt.1));
}