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(void){
  int i,n;
  long long int a, kians=0, guans=0, kisum=0, gusum=0;

  scanf("%d", &n);

  for(i=0;i<n;i++){
    scanf("%lld", &a);
    kisum+=a;
    gusum+=a;
    if(i%2==0){
      if(gusum<=0){
        guans=guans-gusum+1;
        gusum=1;
      }
      if(kisum>=0){
        kians=kians+kisum+1;
        kisum=-1;
      }
    }
    else{
      if(gusum>=0){
        guans=guans+gusum+1;
        gusum=-1;
      }
      if(kisum<=0){
        kians=kians-kisum+1;
        kisum=1;
      }
    }
  }
  if(kians>guans) printf("%lld\n", guans);
  else printf("%lld\n", kians);

  return 0;
}