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 <iostream>
#include <sstream>
#include <regex>
#include <cstdio>
#include <cmath>
#include <cctype>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <functional>

using namespace std;
using ll = long long int;
#define rep(i,n) for(int i = 0; i < n; i++)
#define FOR(i, a, b)  for(int i = (a); i < (b) ; i++)
#define pb push_back
#define SORT(v,n) sort(v, v+n)
#define ALL(x) (x).begin(),(x).end()
#define debug(x) cerr << #x << ": " << x << '\n'
#define elif else if
#define int ll
//const int INF = 100100100;
const int INF = (1LL << 32);
const int MOD = (int)1e9 + 7;
const double EPS = 1e-9;
int dx[8] = { 1, 0, -1, 0, 1, -1, -1, 1 };
int dy[8] = { 0, 1, 0, -1, 1, 1, -1, -1 };
typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;

int n;
vector<int> a;

int solve(bool isFirstPlus) {
	int sum = 0;
	int ans1 = 0;
	bool plus = isFirstPlus;
	for (int i = 0; i < n; i++) {
		sum += a[i];
		if (plus and sum <= 0) {
			while (sum != 1) {
				sum++;
				ans1++;
			}
		}
		else if (!plus and sum >= 0) {
			while (sum != -1) {
				ans1++;
				sum--;
			}
		}
		plus = !plus;
	}
	return ans1;
}

signed main() {
	ios::sync_with_stdio(false);
	cin >> n;
	rep(i, n) {
		int x;
		cin >> x;
		a.pb(x);
	}
	int ans1 = solve(true);
	int ans2 = solve(false);
	cout << min(ans2, ans1) << endl;
	return 0;
}