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>

#define fi first
#define se second
#define sc scanf
#define pr printf
#define pb push_back
#define ll long long
#define fin(s) freopen( s, "r", stdin );
#define fout(s) freopen( s, "w", stdout );

const long long N = 100100;
const long long MX = sqrt(N);
const long long H = 17;
const long long MAGIC = 1000;
const long long mod = 1e9 + 7;

using namespace std;

ll n;
ll a[N];

ll f(int g)
{
        ll s = 0, cnt = 0;
        for(int i = 1; i <= n; i++, g ^= 1){
                if(g == 0){
                        s += a[i];
                        cnt += max(0ll, s + 1);
                        s = min(-1ll, s);
                }
                else{
                        s += a[i];
                        cnt += -min(0ll, s - 1);
                        s = max(1ll, s);
                }
        }
        return cnt;
}

void solve()
{
        cin >> n;
        for(int i = 1; i <= n; i++){
                cin >> a[i];
        }
        cout << min(f(0), f(1)) << endl;
}

bool mtest = false; int main()
{
        //fin("input.txt");
        //fout("output.txt");
        //fin("landscape.in");
        //fout("landscape.out");
        ios_base::sync_with_stdio(0);
        int TE = 1;
        if(mtest)
                cin >> TE;
        while(TE--)
                solve();
        return 0;
}