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<stdio.h>

int main(void){
	long long n,a[131072],r,i,c,d,s;
	scanf("%lld",&n);
	for(i = 1;i <= n;i++){scanf("%lld",&a[i]);}
	s=0;c=0;
	for(i = 1;i <= n;i++){
		s+=a[i];
		if(i%2 == 1 && s <= 0){c+=(1-s);s=1;}
		if(i%2 == 0 && s >= 0){c+=(s-(-1));s=-1;}
	}
	s=0;d=0;
	for(i = 1;i <= n;i++){
		s+=a[i];
		if(i%2 == 1 && s >= 0){d+=(s-(-1));s=-1;}
		if(i%2 == 0 && s <= 0){d+=(1-s);s=1;}
	}
	if(c<d){printf("%d\n",c);}else{printf("%d\n",d);}
	return 0;
}