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 main(void)
{
    int num_integer;
    if (scanf("%d", &num_integer) != 1)
    {
        puts("num_integer input error.");
        return 1;
    }

    int integer, sum_1 = 0, sum_2 = 0, num_operation_1 = 0, num_operation_2 = 0;
    for (int i = 0; i < num_integer; i++)
    {
        if(scanf("%d", &integer) != 1)
        {
            puts("integer input error.");
        }

        if (sum_1 > 0 && (sum_1 + integer) >= 0)
        {
            num_operation_1 += sum_1 + integer + 1;
            sum_1 = -1; 
        }
        else if (sum_1 < 0 && (sum_1 + integer) <= 0) 
        {
            num_operation_1 += -(sum_1 + integer) + 1;
            sum_1 = 1;
        }
        else
        {
            sum_1 += integer;
        }
 
        if (sum_2 > 0 && (sum_2 + integer) >= 0)
        {
            num_operation_2 += sum_2 + integer + 1;
            sum_2 = -1; 
        }
        else if (sum_2 < 0 && (sum_2 + integer) <= 0) 
        {
            num_operation_2 += -(sum_2 + integer) + 1;
            sum_2 = 1;
        }
        else
        {
            num_operation_2 = (integer > 0) ? integer + 1 : -integer + 1; 
            sum_2 = (integer > 0) ? integer : -integer; 
        }
    }

    printf("%d", (num_operation_1 < num_operation_2) ? num_operation_1 : num_operation_2); 

    return 0;
}