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 <bits/stdc++.h>
using namespace std;
#define ll long long
const int maxn=1e5+10;
ll s[maxn];
ll ans[maxn];
int main()
{
    int n,j;
    cin>>n;
    ll sum=0;
    for(int i=1; i<=n; i++)
    {
        cin>>s[i];
    }
    if(s[0])
    {
        for(int i=1; i<n; i++)
        {
            ans[i]=ans[i-1]+s[i];
            if(ans[i]>0)
            {
                if(s[i+1]>=0)
                {
                    sum+=(s[i+1]+ans[i]+1);
                    s[i+1]=-(ans[i]+1);
                }
                else
                {
                    if(abs(s[i+1])>ans[i])
                    {

                    }
                    else
                    {
                        sum+=(s[i+1]+ans[i]+1);
                        s[i+1]=-(ans[i]+1);
                    }
                }
            }
            else if(ans[i]<0)
            {
                if(s[i+1]>0)
                {
                    if(abs(ans[i])<s[i+1])
                    {

                    }
                    else
                    {
                        sum+=(1-ans[i]-s[i+1]);
                        s[i+1]=-ans[i]+1;
                    }
                }
                else
                {
                    sum+=(1-ans[i]-s[i+1]);
                    s[i+1]=-ans[i]+1;
                }
            }
        }
        cout<<sum<<endl;
    }
    else if(!s[0])
    {
        sum=0;
        ll anss=0;
        ans[1]=1;
        s[2]=-2;
        sum+=3;
        for(int i=2; i<n; i++)
        {
            ans[i]=ans[i-1]+s[i];
            if(ans[i]>0)
            {
                if(s[i+1]>=0)
                {
                    sum+=(s[i+1]+ans[i]+1);
                    s[i+1]=-(ans[i]+1);
                }
                else
                {
                    if(abs(s[i+1])>ans[i])
                    {

                    }
                    else
                    {
                        sum+=(s[i+1]+ans[i]+1);
                        s[i+1]=-(ans[i]+1);
                    }
                }
            }
            else if(ans[i]<0)
            {
                if(s[i+1]>0)
                {
                    if(abs(ans[i])<s[i+1])
                    {

                    }
                    else
                    {
                        sum+=(1-ans[i]-s[i+1]);
                        s[i+1]=-ans[i]+1;
                    }
                }
                else
                {
                    sum+=(1-ans[i]-s[i+1]);
                    s[i+1]=-ans[i]+1;
                }
            }
        }
        ans[1]=-1;
        s[2]=2;
        anss+=3;
        for(int i=2; i<n; i++)
        {
            ans[i]=ans[i-1]+s[i];
            if(ans[i]>0)
            {
                if(s[i+1]>=0)
                {
                    anss+=(s[i+1]+ans[i]+1);
                    s[i+1]=-(ans[i]+1);
                }
                else
                {
                    if(abs(s[i+1])>ans[i])
                    {

                    }
                    else
                    {
                        anss+=(s[i+1]+ans[i]+1);
                        s[i+1]=-(ans[i]+1);
                    }
                }
            }
            else if(ans[i]<0)
            {
                if(s[i+1]>0)
                {
                    if(abs(ans[i])<s[i+1])
                    {

                    }
                    else
                    {
                        anss+=(1-ans[i]-s[i+1]);
                        s[i+1]=-ans[i]+1;
                    }
                }
                else
                {
                    anss+=(1-ans[i]-s[i+1]);
                    s[i+1]=-ans[i]+1;
                }
            }
        }
        cout<<min(anss,sum)<<endl;
    }
return 0;
}