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: Accepted)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
	private static final int MOD = (int)Math.pow(10, 9);
	public static void main(String[] args) {
		FastReader sc = new FastReader();
		int n = sc.nextInt();
		int[] nums = new int[n];
		
		for (int i = 0; i < nums.length; i++) {
			nums[i] = sc.nextInt();
		}
		long firstDigitPostive = 0;

		long prefixSum = 0;
		for (int i = 0; i < nums.length; i++) {
			prefixSum += nums[i];
			if (i % 2 == 0) {
				// odd is postive
				if (prefixSum == 0) {
					prefixSum++;
					firstDigitPostive++;
				} else if (prefixSum < 0) {
					firstDigitPostive += (1 - prefixSum);
					prefixSum += 1 - prefixSum;
				}
			} else {
				// even is negative
				if (prefixSum == 0) {
					prefixSum--;
					firstDigitPostive++;
				} else if (prefixSum > 0) {
					firstDigitPostive += (1 + prefixSum);
					prefixSum -= (prefixSum + 1) ;
				}
			}
		}
		
		prefixSum = 0;
		long firstDigitNegative = 0;
		for (int i = 0; i < nums.length; i++) {
			prefixSum += nums[i];
			if (i % 2 == 0) {
				// odd is negative
				if (prefixSum == 0) {
					prefixSum--;
					firstDigitNegative++;
				} else if (prefixSum > 0) {
					firstDigitNegative += (1 + prefixSum);
					prefixSum -= (prefixSum + 1) ;
				}
			} else {
				// even is postive
				if (prefixSum == 0) {
					prefixSum++;
					firstDigitNegative++;
				} else if (prefixSum < 0) {
					firstDigitNegative += (1 - prefixSum);
					prefixSum += 1 - prefixSum;
				}
			}
		}
		
		System.out.println(Math.min(firstDigitPostive, firstDigitNegative));
	}

    static class FastReader {
	    BufferedReader br;
	    StringTokenizer st;
	
	    public FastReader() {
	      br = new BufferedReader(new InputStreamReader(System.in));
	    }
	  
	    String next() { 
	      while (st == null || !st.hasMoreElements()) {
	        try {
	          st = new StringTokenizer(br.readLine());
	        } catch (IOException  e) {
	          e.printStackTrace();
	        }
	      }
	      return st.nextToken();
	    }
	
	    int nextInt() {
	      return Integer.parseInt(next());
	    }
	
	    long nextLong() {
	      return Long.parseLong(next());
	    }
	
	    double nextDouble() { 
	      return Double.parseDouble(next());
	    }
	
	    String nextLine() {
	      String str = "";
	        try{
	            str = br.readLine();
	        } catch (IOException e) {
	            e.printStackTrace();
	        }
	        return str;
	      }
	  }
}