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 <algorithm>
#include <map>
#include <set>
#include <vector>
#include <queue>
#include <cmath>

#define	MOD 1000000007;
#define PI 3.14159265358979323846;
using namespace std;
typedef long long ll;
ll mod = 1000000007;

int main()
{
	int n;
	cin >> n;
	ll a[100000];
	ll c1 = 0;
	ll c2 = 0;

	for (int i = 0; i < n; i++) cin >> a[i];

	ll sum = 0;
	int c = 1;

	//odd number are over 0;
	for (int i = 0; i < n; i++)
	{
		sum += a[i];
		if (sum * c <= 0)
		{
			c1 += abs(sum) + 1;
			sum = c;
		}

		c *= -1;
	}

	//even numbers are over 0
	c = -1;
	sum = 0;
	for (int i = 0; i < n; i++)
	{
		sum += a[i];
		if (c * sum < 0)
		{
			c2 += abs(sum) + 1;
			sum = c;
		}
		c *= -1;
	}

	cout << min(c1, c2) << endl;
	return 0;
}