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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(void){

	int i,n;
	long long int gusum = 0,kisum = 0;
	long long int gucount = 0,kicount = 0,a;

	scanf("%d",&n);

	for(i = 0; i < n; i++){
		scanf("%lld",&a);
		gusum += a;
		kisum += a;

		if(i % 2 == 0){

			if(gusum <= 0){
				gucount += 1 - gusum;
				gusum = 1;
			}
			if(kisum >= 0){
				kicount += 1 + kisum;
				kisum = -1;
			}
		}
		else{

			if(gusum >= 0){
				gucount += 1 + gusum;
				gusum = -1;
			}
			if(kisum <= 0){
				kicount += 1 - kisum;
				kisum = 1;
			}
		}
	}
	if(kicount > gucount){
			printf("%lld\n",gucount);
		}
		else
			printf("%lld\n",kicount);
	
	return 0;
}