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: Wrong Answer)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::*;

#[fastout]
fn main() {
    input! {
        n: usize,
        a: [i64; n]
    }

    let mut ans1 = 0;
    {
        let mut sum = 0;
        for i in 0..n {
            sum += a[i];
            if i % 2 == 0 {
                let dif = if sum > 0 { 0 } else { 1 - sum };
                if sum <= 0 {
                    sum = 1
                }
                ans1 += dif;
            } else {
                let dif = if sum < 0 { 0 } else { sum + 1 };
                if sum > 0 {
                    sum = -1
                }
                ans1 += dif;
            }
        }
    }

    let mut ans2 = 0;
    {
        let mut sum = 0;
        for i in 0..n {
            sum += a[i];
            if i % 2 == 1 {
                let dif = if sum > 0 { 0 } else { 1 - sum };
                if sum <= 0 {
                    sum = 1
                }
                ans2 += dif;
            } else {
                let dif = if sum < 0 { 0 } else { sum + 1 };
                if sum > 0 {
                    sum = -1
                }
                ans2 += dif;
            }
        }
    }

    println!("{}", std::cmp::min(ans1, ans2));
}
*/

fn main() {
    let exe = "/tmp/binA4A6465F";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";