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: Wrong Answer)

#include <limits.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <unistd.h>
#include <math.h>

#define P 1000000007

int comp(const void *a, const void *b){return *(int*)a-*(int*)b;}

int main(void){
	int n, i;
	int a[100001];
	scanf("%d", &n);
	for(i=0; i<n; i++){
		scanf("%d", a+i);
	}
	int n1=0, n2=0;
	{
		int sum=0;
		int f=0;
		for(i=0; i<n; i++){
			sum += a[i];
			if(f){
				if(sum<=0){n1=n1+1-sum; sum=1;}
			}else{
				if(sum>=0){n1=n1+1+sum; sum=-1;}
			}
			f=!f;
		}
	}
	{
		int sum=0;
		int f=1;
		for(i=0; i<n; i++){
			sum += a[i];
			if(f){
				if(sum<=0){n2=n2+1-sum; sum=1;}
			}else{
				if(sum>=0){n2=n2+1+sum; sum=-1;}
			}
			f=!f;
		}
	}
	printf("%ld\n", n1<n2?n1:n2);
}