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;
using llong = long long;
using P = pair<llong, llong>;

#define BE(x) x.begin(), x.end()

const llong inf = llong(1e18)+7;
const llong mod = 1e9+7;

int main(){
	int n;
	vector<llong> a;

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

	llong sum = a[0];
	llong ans = 0;
	for(int i = 1; i < n; i++){
		llong next = sum + a[i];
		if(sum > 0 && next > 0){
			ans += next;
			a[i] -= next;
		}
		if(sum < 0 && next < 0){
			ans += -next;
			a[i] -= next;
		}

		if(sum + a[i] == 0)
			a[i] += (a[i] > 0 ? 1 : -1), ans++;

		sum += a[i];
	}

	for(int i = 0; i < n; i++)
		cerr << a[i] << " ";
	cerr << endl;

	cout << ans << endl;

	return 0;
}