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::{BufRead, Write};
use std::io;

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut s = String::new();
    input.read_line(&mut s).unwrap();
    let _ = s.trim().parse::<usize>().unwrap();
    s.clear();
    input.read_line(&mut s).unwrap();
    let a = s.split_whitespace()
        .map(|s| s.parse::<i64>().unwrap())
        .collect::<Vec<_>>();
    let result = [true, false]
        .iter()
        .map(|&initial| {
            let mut flag = initial;
            let mut total = 0;
            let mut cost = 0usize;
            for &i in &a[0..] {
                total += i;
                if total == 0 || (total > 0) != flag {
                    cost += (total - if flag { 1 } else { -1 }).abs() as usize;
                    total = if flag { 1 } else { -1 };
                }
                flag ^= true;
            }
            cost
        })
        .min()
        .unwrap();
    writeln!(output, "{}", result).unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v = Vec::<u8>::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }
    #[test]
    fn case1() {
        test("4
1 -3 1 0\n",
             "4\n");
    }
    #[test]
    fn case2() {
        test("5
3 -6 4 -5 7\n",
             "0\n");
    }
    #[test]
    fn case3() {
        test("6
-1 4 3 2 -5 4\n",
             "8\n");
    }
}