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 Python (3.4.3) (judge verdict: Wrong Answer)

import numpy as np
n=int(input())
a=list(map(int,input().split()))
r=[0]
for i in range(n):
    r.append(r[i]+a[i])
r.pop(0)
print(r)

pm=[1-2*(i%2) for i in range(n)]
mp=[1-2*((i+1)%2) for i in range(n)]
print(pm)
print(mp)

sum1,sum2=0,0
sousa1,sousa2=0,0

for i in range(n):
    if np.sign(r[i]+sousa1) != pm[i]:
        sum1+=abs(pm[i]-r[i]-sousa1)
        sousa1+=1-2*(i%2)-r[i]
        
for i in range(n):
    if np.sign(r[i]+sousa2) != mp[i]:
        sum2+=abs(mp[i]-r[i]-sousa2)
        sousa2+=1-2*((i+1)%2)-r[i]
        
print(min(sum1,sum2))