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<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

use std::cmp::min;

fn main() {
    let n: usize = read();
    let a: Vec<i64> = read_vec();

    //start with plus
    let mut cnt1: i64 = 0;
    let mut sum = a[0];
    if sum <= 0 {
        cnt1 += 1 - sum;
        sum = 1;
    }
    for i in 1..n {
        if sum > 0 {
            if a[i] + sum < 0 {
                sum += a[i];
            } else {
                cnt1 += a[i] + sum + 1;
                sum = -1;
            }
        } else {
            if a[i] + sum > 0 {
                sum += a[i];
            } else {
                cnt1 += 1 - sum - a[i];
                sum = 1;
            }
        }
    }

    //start with minus
    let mut cnt2: i64 = 0;
    let mut sum = a[0];
    if sum >= 0 {
        cnt2 += 1 + sum;
        sum = -1;
    }
    for i in 1..n {
        if sum > 0 {
            if a[i] + sum < 0 {
                sum += a[i];
            } else {
                cnt2 += a[i] + sum + 1;
                sum = -1;
            }
        } else {
            if a[i] + sum > 0 {
                sum += a[i];
            } else {
                cnt2 += 1 - sum - a[i];
                sum = 1;
            }
        }
    }

    println!("{}", min(cnt1, cnt2));
}