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 (Clang 3.8.0) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define BUF_SIZE 1500000
#define min(a, b) ((a) < (b) ? (a) : (b))

int main(void) {
  char buf[BUF_SIZE];
  FILE *fp = stdin;

  if(!fgets(buf, BUF_SIZE, fp)) return 0;

  int num;
  sscanf(buf, "%d", &num);

  if(!fgets(buf, BUF_SIZE, fp)) return 0;

  char *tmpbuf = buf;
  int i;
  long sum_plus = 0;
  long sum_minus = 0;

  long res_plus = 0;
  long res_minus = 0;
  for(i = 0; i < num; i++) {
    char *tmp = strtok(tmpbuf, " ");
    long n = strtol(tmp, NULL, 10);
    sum_plus += n;
    sum_minus += n;
    if (i%2) { // odd
      // start_plus requires sum of minus
      if(sum_plus >= 0) {
        res_plus += sum_plus + 1;
        sum_plus = -1;
      }
      if(sum_minus <= 0) {
        res_minus += 1 - sum_minus; // -1 - n
        sum_minus = 1;
      }
    } else { // even
      if(sum_plus <= 0) {
        res_plus += 1 - sum_plus; // -1 - n
        sum_plus = 1;
      }
      if(sum_minus >= 0) {
        res_minus += sum_minus + 1;
        sum_minus = -1;
      }
    }
    tmpbuf = NULL;
  }

  long res = min(res_plus, res_minus);
  printf("%ld\n", res);

  return 0;
}