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<stdlib.h>
#include<string.h>
#include<stdint.h>
#include<stdbool.h>
#include<tgmath.h>
#include<sys/queue.h>
#include<time.h>
#define ll long long
#define min(a, b) ((a) > (b) ? (b) : (a))
#define max(a, b) ((a) > (b) ? (a) : (b))
#define miin(a, b, c) min((a), min((b), (c)))
#define maax(a, b, c) max((a), max((b), (c)))
#define mod 1000000007

ll n, a[111111], hoge, huga, nyaa = 0, nyan = 0;

main(){
    scanf("%lld", &n);
    for(int i=0; i<n; i++){
        scanf("%lld", &a[i]);
    }
    if(!a[0]){
        hoge = 1;
        huga = -1;
        nyaa = nyan = 1;
    }else {
        hoge = max(a[0], -a[0]);
        huga = min(a[0], -a[0]);
        nyaa += abs(a[0] - hoge);
        nyan += abs(a[0] - huga);
    }
    int p = 1;
    //printf("%d %d %d %d\n", hoge, huga, nyaa, nyan);
    for(int i=1; i<n; i++){
        hoge += a[i];
        if(p){
            if(hoge >= 0){
                nyaa += hoge + 1;
                hoge = -1;
            }
        }else {
            if(hoge <= 0){
                nyaa += 1 - hoge;
                hoge = 1;
            }
        }
        huga += a[i];
        if(p){
            if(huga <= 0){
                nyan += 1 - huga;
                huga = 1;
            }
        }else {
            if(huga >= 0){
                nyan += huga + 1;
                huga = -1;
            }
        }
        p ^= 1;
        //printf("%d %d %d %d\n", hoge, huga, nyaa, nyan);
    }
    printf("%lld\n", min(nyaa, nyan));
    return 0;
}