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 <cmath>
#include <cassert>

int main(int argc, char const* argv[])
{
    uint64_t n;
    std::cin >> n;

    int64_t sum, current;
    std::cin >> current;
    sum = current;

    uint64_t result = 0;
    if(current == 0)
    {
        sum = -1;
        result++;
    }

    bool is_sum_negative = sum < 0;

    for (int i = 1; i < n; ++i)
    {
        std::cin >> current;
        sum += current;

        /* std::cout << "current: " << sum << std::endl; */
        auto tmp = std::abs(sum) + 1;
        if(is_sum_negative)
        {
            if(sum <= 0)
            {
                sum += tmp;
                result += tmp;

                /* std::cout << result << std::endl; */

                assert(sum == 1);
            }
        }
        else
        {
            if(sum >= 0)
            {
                sum -= tmp;
                result += tmp;
                /* std::cout << result << std::endl; */

                assert(sum == -1);
            }
        }
        /* std::cout << "after: " << sum << std::endl; */

        is_sum_negative = !is_sum_negative;
    }

    std::cout << result << std::endl;
}