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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include<iostream>
#include<vector>

#define ll long long

using namespace std;

int main(){
    int n, a, i;
    ll s = 0, news, count1 = 0, count2 = 0;

    cin >> n;
    vector<ll> as(n);

    for(int i = 0; i < n; i++){
        cin >> a;
        s += a;
        as[i] = s;
    }

    i = 0;
    s = 0;
    while(i < n){
        news = as[i] + s;
        if(news > -1){
            s -= news + 1;
            count1 += news + 1;
        }
        if(++i >= n) break;

        news = as[i] + s;
        if(news < 1){
            s += 1 - news;
            count1 += 1 - news;
        }
        i++;
    }

    i = 0;
    s = 0;
    while(i < n){
        news = as[i] + s;
        if(news < 1){
            s += 1 - news;
            count2 += 1 - news;
        }
        if(++i >= n) break;

        news = as[i] + s;
        if(news > -1){
            s -= news + 1;
            count2 += news + 1;
        }
        i++;
    }

    cout << (count1 < count2 ? count1 : count2) << endl;
}