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<bits/stdc++.h>
using namespace std;
int MOD = 1000000007;
//g++ -std==c++14
//setprecision(10)
int main(){
    int n;  cin >> n;
    int a[n];
    for(int i = 0; i < n; i++)  cin >> a[i];
    int sum = a[0], cnt = 0; 
    for(int i = 1; i < n; i++){
        if(sum + a[i] == 0){
            sum = sum > 0 ? -1 : 1;
            cnt++;
        }
        else if( (sum > 0 && sum + a[i] > 0) || (sum < 0 && sum + a[i] < 0) ){
            cnt += abs(sum + a[i]) + 1;
            sum = sum > 0 ? -1 : 1;
        }
        else{
            sum += a[i];
        }
    }
    cout << cnt << endl;
}