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 <cmath>
#include <vector>
using namespace std;

typedef long long ll;

int N;
vector<int> A;
int sum;
ll trn;

void calcu(int p, char s) {
	if (p >= N)
		return;
	int x = A[p];
	if (s == '+') {
		if (sum + x <= 0)
			x = 1 - sum;
		sum += x;
		trn += abs(A[p] - x);
		calcu(++p, '-');
	}
	else {
		if (sum + x > 0)
			x = -1 - sum;
		sum += x;
		trn += abs(A[p] - x);
		calcu(++p, '+');
	}
}

int main(void) {
	cin >> N;
	A.resize(N);
	for (int i = 0; i < N; ++i)
		cin >> A[i];

	sum = (A[0] > 0) ? A[0] : 1;
	trn = (A[0] > 0) ? 0 : 1 - A[0];
	calcu(1, '-');
	ll a = trn;

	sum = (A[0] < 0) ? A[0] : -1;
	trn = (A[0] < 0) ? 0 : 1 + A[0];
	calcu(1, '+');
	ll b = trn;

	ll ans = (a < b) ? a : b;
	cout << ans << '\n';
	return 0;
}