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>
#include <stdlib.h>

int sequence(int n, int* a)
{
  int i,sum,count1,count2;
  sum = 0;
  count1 = 0;
  for(i = 0; i < n; i++){
    sum += a[i];
    if(i % 2 == 1 && sum <= 0){
      count1 += (1-sum);
      sum = 1;
    }
    if(i % 2 == 0 && sum >= 0){
      count1 += sum+1;
      sum = -1;
    }
  }
  sum = 0;
  count2 = 0;
  for(i = 0; i < n; i++){
    sum += a[i];
    if(i % 2 == 1 && sum >= 0){
      count2 += sum+1;
      sum = -1;
    }
    if(i % 2 == 0 && sum <= 0){
      count2 += 1-sum;
      sum = 1;
    }
  }
  if(count1 < count2){
    return count1;
  }else{
    return count2;
  }
}

int main()
{
  int n,i,result;
  if(scanf("%d", &n) < 1){
      exit(1);
  }
  int a[n];
  for(i = 0; i < n; i++){
    if(scanf("%d", &a[i]) < 1){
      exit(1);
    }
  }
  result = sequence(n, a);
  printf("%d\n",result);
  return 0;
}