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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.io.*;
import java.util.*;

class Main{
    public static void main(String[] args){
        solve();
    }

    public static void solve(){
        Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		int[] b = new int[n];
		for (int i=0; i<n; i++) {
			a[i] = sc.nextInt();
			b[i] = a[i];        	
		}        
		long ans = 0;
		int count = a[0];
		for(int i=1;i<n;i++){
			if(count>=0 && count+a[i]>=0){
				int tmp = a[i];
				a[i] = -1 - count;
				ans += (int)Math.abs(tmp - a[i]);

			}
			else if(count<0 && count+a[i]<0){
				int tmp = a[i];
				a[i] = 1 - count;
				ans += (int)Math.abs(tmp - a[i]);
			}
			if(i==n-1 && count+a[i]==0){
				ans += 1;
				break;
			}
			count += a[i];
		}
		long bans =0;
		if(b[0]>=0){
			int x = 1 + b[0];
			b[0] = -1;
			bans = x;
		}
		else{
			int x = -b[0];
			b[0] = 0;
			bans = x;
		}
		count = b[0];
		for(int i=1;i<n;i++){
			if(count>=0 && count+b[i]>=0){
				int tmp = b[i];
				b[i] = -1 - count;
				bans += (int)Math.abs(tmp - b[i]);

			}
			else if(count<0 && count+b[i]<0){
				int tmp = b[i];
				b[i] = 1 - count;
				bans += (int)Math.abs(tmp - b[i]);
			}
			if(i==n-1 && count+b[i]==0){
				bans += 1;
				break;
			}
			count += b[i];
		}
		System.out.println(Math.min(ans, bans));
    }
}