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: Wrong Answer)

#include<iostream>
#include<string>
#include<vector>
#include<list>
#include<cmath>
#include<algorithm>
#include<cstdio>
#include<set>
#include<queue>
using namespace std;

typedef long long ll;

int main() {
  int n; cin >> n;
  ll a[100010];
  ll sum = 0,cnt = 0,sum2 = 0,cnt2 = 0;
  for ( int i = 0; i < n; i++ ) cin >> a[i];
  bool nextpo = false,nextpo2 = false;
  bool nextne = false,nextne2 = false;
  sum = a[0];
  if ( sum < 0 ) {
    nextpo = true;
    nextne2 = true;
    cnt2 += abs(sum2)+1;
    sum2 += abs(sum2)+1;
  }
  else if ( sum > 0 ) {
    nextne = true;
    nextpo2 = true;
    cnt2 += sum2+1;
    sum2 -= sum2+1;
  }

  
  for ( int i = 1; i < n; i++ ) {

    if(nextpo) {
      nextpo = false;
      nextne = true;
      sum += a[i];

      if ( sum == 0 ) {
	sum++;
	cnt++;
      } else if ( sum < 0 ) {
	cnt += abs(sum)+1;	
	sum += abs(sum)+1;
      }
    }else if ( nextne){
      nextpo = true;
      nextne = false;
      sum += a[i];

      if ( sum == 0 ) {
	sum--;
	cnt++;
      } else if ( sum > 0 ) {
	cnt += sum+1;	
	sum -= sum+1;
      }
    }
  }

  for ( int i = 1; i < n; i++ ) {

    if(nextpo2) {
      nextpo2 = false;
      nextne2 = true;
      sum2 += a[i];

      if ( sum2 == 0 ) {
	sum2++;
	cnt2++;
      } else if ( sum2 < 0 ) {
	cnt2 += abs(sum2)+1;	
	sum2 += abs(sum2)+1;
      }
    }else if ( nextne2){
      nextpo2 = true;
      nextne2 = false;
      sum2 += a[i];

      if ( sum2 == 0 ) {
	sum2--;
	cnt2++;
      } else if ( sum2 > 0 ) {
	cnt2 += sum2+1;	
	sum2 -= sum2+1;
      }
    }
  }
  //cout << cnt << " " << cnt2 << endl;
  cout << min(cnt,cnt2) << endl;
  return 0;
}