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 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

int abs(int num)
{
    return (num > 0) ? num : -num;
}

int main()
{
    int n;  scanf("%d", &n);
    int A[n];
    int i;
    int sum = 0;
    int ans = 0;

    for(i = 0; i < n; i++){
        scanf("%d", &A[i]);
    }

    for(i = 0; i < n - 1; i++){
        sum += A[i];
        if(sum > 0){
            if(sum >= -A[i + 1]){
            ans += abs(sum + A[i + 1] + 1);
            A[i + 1] -= abs(sum + A[i + 1] + 1);
            }
        }
        else{
            if(sum <= -A[i + 1]){
            ans += abs(sum + A[i + 1] - 1);
            A[i + 1] += abs(sum + A[i + 1] + 1);
            }
        }
    }

    printf("%d\n", ans);

    return 0;
}