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 <stdio.h>
#include <algorithm>

using namespace std;

#define MAXN 200005

typedef long long lint;

int N, A[MAXN];

lint solve() {
	lint ans = 0ll;
	int s = 0;
	for(int i = 0; i < N; i++) {
		s += A[i];
		if(i % 2) {
			int d = max(0, 1 - s);
			ans += d;
			s += d;
		}
		else {
			int d = max(0, s + 1);
			ans += d;
			s -= d;
		}
		//printf("i = %d, s = %d, ans = %d\n", i, s, ans);
	}
	return ans;
}

int main() {
	scanf("%d", &N);
	for(int i = 0; i < N; i++) scanf("%d", A + i);

	lint ans = solve();
	for(int i = 0; i < N; i++) A[i] *= -1;
	printf("%lld", min(ans, solve()));
	return 0;
}