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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using static System.Console;
using static System.Convert;
using static System.Math;
 
class Program
{
    static void Main(string[] args)
    {
       int n = int.Parse(Console.ReadLine());
      int[] arr = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
      long[] arrSum = new long[n];
      long sum_Plus = 0;
      long sum_minus = 0;
      bool isChange = false;
      bool isChange_minus = false;
      long nPreSum_Plus = 0;
      long nPreSum_minus = 0;
      for (int i = 0; i < n; i++)
      {
        if (i == 0)
        {
          arrSum[0] = arr[0];
          nPreSum_minus = arr[0];
          nPreSum_Plus = arr[0];
        }
        else
        {
          arrSum[i] = (arrSum[i - 1] + arr[i]);
        }

        #region //plusStart
          if (i % 2 == 0)
          {
            if (!isChange)
            {
              //一回も変更していない
              if (arrSum[i] > 0)
              {
                //isChange = false;
              }
              else if (arrSum[i] < 0)
              {
                long tmpcnt = (1 - arrSum[i]);
                sum_Plus += tmpcnt;
                nPreSum_Plus = 1;
                isChange = true;
              }
              else
              {
                sum_Plus += 1;
                nPreSum_Plus = 1;
                isChange = true;
              }
            }
            else
            {
              //一回でも変更したとき　arrSum[i-1]=-1
              long tmpsum = (nPreSum_Plus) + arr[i];
              if (0<tmpsum)
              {
                //isChange = false;
                nPreSum_Plus = tmpsum;
              }
              else if (tmpsum < 0)
              {
                long tmpcnt = Math.Abs(1 - (nPreSum_Plus));
                sum_Plus += tmpcnt;
                nPreSum_Plus = nPreSum_Plus + arr[i];
              }
              else
              {
                sum_Plus += 1;
                nPreSum_Plus = 1;
              }
            }
          }
        else
        {
          //奇数インデックス⇒マイナスにする
          if (!isChange)
          {
            //一回も変更していない
            if (arrSum[i] < 0)
            {
              //isChange = false;
            }
            else if (arrSum[i] > 0)
            {
              long tmpcnt = (arrSum[i] - (-1));
              sum_Plus += tmpcnt;
              nPreSum_Plus = -1;
              isChange = true;
            }
            else
            {
              sum_Plus += 1;
              nPreSum_Plus = -1;
              isChange = true;
            }
          }
          else
          {
            //一回でも変更したとき⇒arrSum[i-1]=1;
            long tmpSum = nPreSum_Plus + arr[i];
            if (tmpSum < 0)
            {
              //isChange = false;
              nPreSum_Plus= tmpSum;
            }
            else if (0<tmpSum)
            {
              long tmpcnt = (Math.Abs((-1)-nPreSum_Plus));
              sum_Plus += tmpcnt;
              nPreSum_Plus = nPreSum_Plus + arr[i];
            }
            else
            {
              sum_Plus += 1;
              nPreSum_Plus = -1;
            }
          }
        }
        #endregion

          #region //minusStart
          if (i % 2 == 1)
          {
            if (!isChange_minus)
            {
              //一回も変更していない
              if (arrSum[i] > 0)
              {
                //isChange_minus = false;
              }
              else if (arrSum[i] < 0)
              {
                long tmpcnt = (1 - arrSum[i]);
                sum_minus += tmpcnt;
                nPreSum_minus = 1;
                isChange_minus = true;
              }
              else
              {
                sum_minus += 1;
                nPreSum_minus = 1;
                isChange_minus = true;
              }
            }
            else
            {
              //一回でも変更したとき　arrSum[i-1]=-1
              long tmpsum = (nPreSum_minus) + arr[i];
              if (0 < tmpsum)
              {
                //isChange_minus = false;
                nPreSum_minus= tmpsum;
              }
              else if (tmpsum < 0)
              {
                long tmpcnt = Math.Abs(1 - (nPreSum_minus));
                sum_minus += tmpcnt;
                nPreSum_minus = nPreSum_minus + arr[i];
              }
              else
              {
                sum_minus += 1;
                nPreSum_minus = 1;
              }
            }
          }
        else
        {
          //奇数インデックス⇒マイナスにする
          if (!isChange_minus)
          {
            //一回も変更していない
            if (arrSum[i] < 0)
            {
              //isChange_minus = false;
            }
            else if (arrSum[i] > 0)
            {
              long tmpcnt = (arrSum[i] - (-1));
              sum_minus += tmpcnt;
              nPreSum_minus = -1;
              isChange_minus = true;
            }
            else
            {
              sum_minus += 1;
              nPreSum_minus = -1;
              isChange_minus = true;
            }
          }
          else
          {
            //一回でも変更したとき⇒arrSum[i-1]=1;
            long tmpSum = nPreSum_minus + arr[i];
            if (tmpSum < 0)
            {
              //isChange_minus = false;
              nPreSum_minus = tmpSum;
            }
            else if (0 < tmpSum)
            {
              long tmpcnt = (Math.Abs((-1) - nPreSum_minus));
              sum_minus += tmpcnt;
              nPreSum_minus = nPreSum_minus + arr[i];
            }
            else
            {
              sum_Plus += 1;
              nPreSum_minus = -1;
            }
          }
        }
        #endregion
      }
      var ans = sum_minus <= sum_Plus ? sum_minus : sum_Plus;
      Console.WriteLine(ans);   
    }
}