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: Accepted)

#include <stdio.h>

long min(long a,long b){
  if(a < b){
    return a;
  }
  return b;
}

int main(void){
  int N;
  scanf("%d",&N);

  long sum,a[N];
  long ans = 0;
  long sample = 0;

  for(int i = 0;i < N;i++) scanf("%ld",&a[i]);

  sum = 0;
  for(int i = 0;i < N;i++){
    sum += a[i];
    if(i%2 == 0){
      if(sum <= 0){
        ans += 1-sum;
        sum = 1;
      }
    }else{
      if(sum >= 0){
        ans += 1+sum;
        sum = -1;
      }
    }
  }

  sum = 0;
  for(int i = 0;i < N;i++){
    sum += a[i];
    if(i%2 != 0){
      if(sum <= 0){
        sample += 1-sum;
        sum = 1;
      }
    }else{
      if(sum >= 0){
        sample += 1+sum;
        sum = -1;
      }
    }
  }

  printf("%ld\n",min(ans,sample));

  return 0;
}