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<algorithm>
#include<string>
#include<cmath>
#include<vector>
#include<map>
using namespace std;
//わからん
int main() {
    int n;
    cin >> n;
    long long a[100001];
    long long sum1 = 0;
    long long sum2 = 0;
    for(int i = 0; i < n; i++) {
        cin >> a[i];
    }

    long long ans1 = 0;
    long long ans2 = 0;

    for(int i = 0; i < n; i++){
        sum1 += a[i];
        if(i % 2 == 0 && sum1 <= 0){
            ans1 += (1 - sum1); 
            sum1 += (1 - sum1);
            if(sum1 == 0) {
                sum1++;
                ans1++;
            }
        }

        else if(i % 2 == 1 && sum1 >= 0){
            ans1 += (sum1 + 1);
            sum1 -= (1 + sum1);
            if(sum1 == 0) {
                sum1--;
                ans1++;
            }
        }
    }


    for(int i = 0; i < n; i++){
        sum2 += a[i];

        if(i % 2 == 0 && sum2 >= 0){
            ans2 += (sum2 + 1); 
            sum2 -= (1 + sum2);
            if(sum2 == 0) {
                sum2--;
                ans2++;
            }
        }
        else if(i % 2 == 1 && sum2 <= 0){
            ans2 += (1 - sum2);
            sum2 += (1 - sum2);
            if(sum2 == 0) {
                sum2++;
                ans2++;
            }
        }
    }

    if(sum2 == 0) ans2++;
    
    if(ans1 >= ans2) cout << ans2 << endl;
    else cout << ans1 << endl;

    return 0;
}