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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <vector>
#include <string>
#include <numeric>
using namespace std;

typedef long long ll;

int main(){

    int n;
    cin >> n;

    vector<long long> v(n);
    for(int i = 0; i < n; i++){
        cin >> v[i];
    }

    ll ans = 0;
    ll ans_1 = 100000000;
    ll sum = v[0];
    ll sum_old;
    if(sum == 0){

        ans = 0;
        sum = 1;
        ans += 1;
        sum_old = 1;
        for(int i = 1; i < n; i++){
            sum += v[i];
            if(sum_old < 0){
                if(sum <= 0){
                    ans += 1 - sum;
                    sum = 1;
                }
            }
            if(sum_old > 0){
                if(sum >= 0){
                    ans += 1 + sum;
                    sum = -1;
                }
            }
            sum_old = sum;
        }    
        ans_1 = min(ans_1, ans);

        ans = 0;
        sum = -1;
        ans += 1;
        sum_old = -1;
        for(int i = 1; i < n; i++){
            sum += v[i];
            if(sum_old < 0){
                if(sum <= 0){
                    ans += 1 - sum;
                    sum = 1;
                }
            }
            if(sum_old > 0){
                if(sum >= 0){
                    ans += 1 + sum;
                    sum = -1;
                }
            }
            sum_old = sum;
        }    
        ans_1 = min(ans_1, ans);

    }

        ans = 0;
        sum = v[0];
        sum_old = sum;
        for(int i = 1; i < n; i++){
            sum += v[i];
            if(sum_old < 0){
                if(sum <= 0){
                    ans += 1 - sum;
                    sum = 1;
                }
            }
            if(sum_old > 0){
                if(sum >= 0){
                    ans += 1 + sum;
                    sum = -1;
                }
            }
            sum_old = sum;
        }    
        ans_1 = min(ans_1, ans);

    cout << ans_1 << endl;

}