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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use itertools::Itertools;
use num::clamp;
use proconio::{input, marker::*, fastout};
use superslice::*;

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

    let mut resp = 0i64;
    let mut sum = 0;
    let mut plus = true;
    for i in 0..n {
        let sum2 = sum + a[i];
        if plus && sum2 <= 0 {
            resp += 1 - sum2;
            sum = 1;
        } else if !plus && sum2 >= 0 {
            resp += sum2 + 1;
            sum = -1;
        } else {
            sum = sum2;
        }
        plus = !plus;
    }

    let mut resm = 0i64;
    let mut sum = 0;
    let mut plus = false;
    for i in 0..n {
        let sum2 = sum + a[i];
        if plus && sum2 <= 0 {
            resm += 1 - sum2;
            sum = 1;
        } else if !plus && sum2 >= 0 {
            resm += sum2 + 1;
            sum = -1;
        } else {
            sum = sum2;
        }
        plus = !plus;
    }
    
    let ans = min(resp, resm);
    println!("{}", ans);
}