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 <iostream>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <functional>
#include <vector>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <bitset>
#include <cassert>
#include <exception>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> P;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<string> vs;
typedef vector<P> vp;
#define rep(i,a,n) for(ll i = (a);i < (n);i++)
#define per(i,a,n) for(ll i = (a);i > (n);i--)
#define lep(i,a,n) for(ll i = (a);i <= (n);i++)
#define pel(i,a,n) for(ll i = (a);i >= (n);i--)
#define clr(a,b) memset((a),(b),sizeof(a))
#define pb push_back
#define mp make_pair
#define all(c) (c).begin(),(c).end()
#define sz size()
#define print(X) cout << (X) << endl
const ll INF = 1e+9+7;
ll n,m,l;
string s,t;
ll d[200010],dp[500][500];
vll start,goal;

int main(){
  cin >> n;
  rep(i,0,n)cin >> d[i];
  ll x = 0,y = 0;
  ll p = 0,q = 0;
  rep(i,0,n){
    x += d[i];
    if(i % 2 == 0){
      if(x <= 0){
        p += -x + 1;
        x = 1;
      }
    }else{
      if(x >= 0){
        p += x + 1;
        x = -1;
      }
    }
  }
  rep(i,0,n){
    y += d[i];
    if(i % 2 != 0){
      if(y <= 0){
        q += -y + 1;
        y = 1;
      }
    }else{
      if(y >= 0){
        q += y + 1;
        y = -1;
      }
    }
  }
  print(min(p,q));
  return 0;
}