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>
#include <string.h>
#include <stdlib.h>
#define swap(type,a,b) do{type t=a;a=b;b=t;}while(0);
#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define INF 100000000
#define FOR(i,a,n) for(i=a;i<n;i++)
#define ll long long

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

int a[100000];
ll sum[100000];

int main(void)
{
    int n,i;
    ll k=0,ans=0;
	scanf("%d",&n);
	FOR(i,0,n){
	    scanf("%d",&a[i]);
	    sum[i]=a[i];
	    if(i!=0) sum[i]+=sum[i-1];
	}
	for(i=0;a[i]==0;i++,ans++);
	for(;i<n-1;i++){
	    if(sum[i]+k>0&&sum[i+1]+k>=0){
	        ans += (sum[i+1]+k+1);
	        k -= (sum[i+1]+1);
	    }
	    else if(sum[i]+k<0&&sum[i+1]+k<=0){
	        ans += (-(sum[i+1]+k)+1);
	        k += (-(sum[i+1]+k)+1);
	    }
	}
	printf("%lld\n",ans);
	return 0;
}