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>
int main(){
  int n;
  long a,sum[100000],cnt[2]={},b;
  scanf("%d",&n);
  scanf("%ld",&a);
  sum[0]=a;
  for(int i=1;i<n;i++){
    scanf("%ld",&a);
    sum[i]=sum[i-1]+a;
  }
  b=0;
  for(int i=0;i<n;i++){
    if(i%2==0&&sum[i]+b>=0){
      cnt[0]+=sum[i]+b+1;
      b-=sum[i]+b+1;
    }
    else if(i%2==1&&sum[i]+b<=0){
      cnt[0]-=sum[i]+b;
      cnt[0]++;
      b+=1-(sum[i]+b);
    }
  }
  b=0;
  for(int i=0;i<n;i++){
    if(i%2==0&&sum[i]+b<=0){
      cnt[1]-=sum[i]+b;
      cnt[1]++;
      b+=1-(sum[i]+b);
    }
    else if(i%2==1&&sum[i]+b>=0){
      cnt[1]+=sum[i]+b+1;
      b-=sum[i]+b+1;
    }
  }
  if(cnt[0]<cnt[1]) printf("%ld\n",cnt[0]);
  else printf("%ld\n",cnt[1]);
}