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 <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i = 0; i < (int)n; i++)
using ll = long long;

int main(){
  int n;
  cin >> n;
  ll a[n];
  rep(i,n) cin >> a[i];
  ll c = 0, d = 0, s = 0, t = 0;
  rep(i,n) {
    s += a[i]; t += a[i];
    if(i % 2 == 0) {
      if(s <= 0) {
        c += 1 - s;
        s = 1;
      } 
      if(t >= 0) {
        d += t + 1;
        t = -1;
      }
    } else {
      if(s >= 0) {
        c += s + 1;
        s = -1;
      }
      if(t <= 0) {
        d += 1 - t;
        t = 1;
      }
    }
  }
  cout << min(c,d) << endl;
  return 0;
}