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 <sstream>
#include <vector>
#include <map>
#include <set>
#include <algorithm>
#include <queue>
#include <cfloat>
#include <cmath>
#include <functional>
#include <forward_list>
#include <list>


#define rep(i,n) for(int i=0;i<n;i++)

using namespace std;


class Main {
public:
	int getAns(vector<int> as) {
		int sum = 0;
		int ans = 0;
		sum += as[0];
		for (int i = 1;i < as.size();i++) {
			if (sum * (as[i] + sum) >= 0) {
				int new_a = (sum * (-1)) + (sum > 0 ? -1 : 1);
				ans += abs(new_a - as[i]);
				as[i] = new_a;
			}
			sum += as[i];
		}
		return ans;
	}
};

int main(void) {
	Main main;
	vector<int> as;
	int n;

	cin >> n;
	rep(i, n) {
		int inp;
		cin >> inp;
		as.push_back(inp);
	}

	cout << main.getAns(as) << endl;

	return 0;
}