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 <cstdio>
long long n, s, t, a[100005], b[100005];
int main() {
	int i;
	scanf("%lld", &n);
	for(i=1; i<=n; i++) scanf("%lld", &a[i]), b[i]=a[i];
	for(i=1; i<=n; i++) {
		a[i] += a[i-1];
		if(i%2) {
			if(a[i]<=0) s += 1-a[i], a[i]=1;
		} else {
			if(a[i]>=0) s += a[i]+1, a[i]=-1;
		}
	}
	for(i=1; i<=n; i++) {
		b[i] += b[i-1];
		if(i%2) {
			if(b[i]>=0) t += b[i]+1, b[i]=-1;
		} else {
			if(b[i]<=0) t += 1-b[i], b[i]=1;
		}
	}
	printf("%lld", std::min(s,t));
	return 0;
}