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 <vector>
#include <cassert>
#include <algorithm>
#include <functional>
#include <cmath>
#include <queue>
#include <set>
#include <stack>
#include <deque>
#include <map>
#include <iomanip>
#include <limits>
using ll = long long;
using ld = long double;
int MOD = 1e9 + 7;
using namespace std;
struct UnionFind
{
    vector<int> par; // par[i]:iの親の番号　(例) par[3] = 2 : 3の親が2

    UnionFind(int N) : par(N)
    { //最初は全てが根であるとして初期化
        for (int i = 0; i < N; i++)
            par[i] = i;
    }

    int root(int x)
    { // データxが属する木の根を再帰で得る：root(x) = {xの木の根}
        if (par[x] == x)
            return x;
        return par[x] = root(par[x]);
    }

    void unite(int x, int y)
    {                     // xとyの木を併合
        int rx = root(x); //xの根をrx
        int ry = root(y); //yの根をry
        if (rx == ry)
            return;   //xとyの根が同じ(=同じ木にある)時はそのまま
        par[rx] = ry; //xとyの根が同じでない(=同じ木にない)時：xの根rxをyの根ryにつける
    }

    bool same(int x, int y)
    { // 2つのデータx, yが属する木が同じならtrueを返す
        int rx = root(x);
        int ry = root(y);
        return rx == ry;
    }
};
int main(){
    ll n;cin>>n;
    int sum=0;
    int reg_1=0;
    vector<int> vec(n);
    for(int i=0;i<n;i++){
        cin>>vec[i];
    }
    for(int i=0;i<n;i++){
        if(i%2==0){
            sum+=vec[i];
            if(sum<=0){
                reg_1+=(1-sum);
                sum=1;
            }
        }else{
            sum+=vec[i];
            if(sum>=0){
                reg_1+=(sum+1);
                sum=-1;
            }
        }
    }
    sum=0;
    int reg_2=0;
    for(int i=0;i<n;i++){
        if(i%2==1){
            sum+=vec[i];
            if(sum<=0){
                reg_2+=(1-sum);
                sum=1;
            }
        }else{
            sum+=vec[i];
            if(sum>=0){
                reg_2+=(sum+1);
                sum=-1;
            }
        }
    }
    cout<<min(reg_1,reg_2)<<endl;
}