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)

#![allow(unused_mut)]
#![allow(non_snake_case)]
#![allow(unused_imports)]
use std::collections::HashSet;
use std::collections::HashMap;
use std::collections::BTreeSet;
use std::collections::VecDeque;
use std::cmp::{max, min};

use std::io::prelude::*;

fn input<T>() -> T
    where T: std::str::FromStr {
    let stdin = std::io::stdin();
    let token: String = stdin
        .lock()
        .bytes()
        .map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().unwrap()
}

fn main() {
    let n: usize = input();
    let mut a_s: Vec<i32> =
        (0..n).map(|_| input()).collect();
    let mut p0 = 0;
    let mut p1 = 0;
    for i in 0..n {
        if i % 2 == 0 {
            p0 += a_s[i];
        } else {
            p1 += a_s[i];
        }
    }
    let mut cnt = 0;
    if p0 < p1 {
        for i in 0..n {
            if a_s[i] == 0 {
                cnt += 1;
            }
            if i % 2 == 0 {
                if a_s[i] > 0 {
                    cnt += a_s[i] + 1
                }
            } else {
                if a_s[i] < 0 {
                    cnt += a_s[i] + 1
                }
            }
        }
    } else {
        for i in 0..n {
            if a_s[i] == 0 {
                cnt += 1;
            }
            if i % 2 == 1 {
                if a_s[i] > 0 {
                    cnt += a_s[i] + 1
                }
            } else {
                if a_s[i] < 0 {
                    cnt += a_s[i] + 1
                }
            }
        }
    }
    println!("{}", cnt);
}