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::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

use std::cmp::min;

fn main() {
    let n: usize = read();
    let mut a: Vec<i64> = vec![];
    for _ in 0..n {
        let ai = read();
        a.push(ai);
    }

    // first is -
    let mut flag = -1;
    let mut sum = 0;
    let mut ans1 = 0;
    for i in 0..a.len() {
        let ai = a[i];
        sum += ai;
        if flag == -1 && sum >= 0 {
            ans1 += (sum + 1).abs();
            sum = -1;
        }
        if flag == 1 && sum <= 0 {
            ans1 += (1 - sum).abs();
            sum = 1;
        }
        flag = -flag;
    }
    let mut flag = 1;
    let mut sum = 0;
    let mut ans2 = 0;
    for i in 0..a.len() {
        let ai = a[i];
        sum += ai;
        if flag == -1 && sum >= 0 {
            ans2 += (sum + 1).abs();
            sum = -1;
        }
        if flag == 1 && sum <= 0 {
            ans2 += (1 - sum).abs();
            sum = 1;
        }
        flag = -flag;
    }
    println!("{}", min(ans2, ans1));

    // first is +
}