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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <cstdio>
#include <cmath>
#include <vector>
using namespace std;

vector<int> num;

long long sequence(int s1, long long c1, int s2, long long c2) {
  for (int i = 1; i < num.size(); i++) {
    if (s1 > 0) {
      if (s1 + num[i] >= 0) {
        c1 += 1 + num[i] + s1;
        s1 = -1;
      } else {
        s1 += num[i];
      }
    } else {
      if (s1 + num[i] <= 0) {
        c1 += 1 - num[i] - s1;
        s1 = 1;
      } else {
        s1 += num[i];
      }
    }
    if (s2 > 0) {
      if (s2 + num[i] >= 0) {
        c2 += 1 + num[i] + s2;
        s2 = -1;
      } else {
        s2 += num[i];
      }
    } else {
      if (s2 + num[i] <= 0) {
        c2 += 1 - num[i] - s2;
        s2 = 1;
      } else {
        s2 += num[i];
      }
    }
  }
  
  return min(c1, c2);
}

int main() {
  int n; scanf("%d", &n);
  
  num.resize(n);
  for (int i = 0; i < n; i++) scanf("%d", &num[i]);
  
  long long ans;
  
  if (num[0] == 0) {
    ans = sequence(1, 1, -1, 1);
  } else if (num[0] > 0) {
    ans = sequence(num[0], 0, -1, num[0] + 1);
  } else {
    ans = sequence(1, abs(num[0]) + 1, num[0], 0);
  }
  
  printf("%lld", ans);
}