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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n=int(input())
l=[int(i) for i in input().split()]
sm=l[0]
req=0 
pr=1 
if sm>0:
    pass 
else:
    req+=-sm+1 
    sm=1 
for i in range(1,n):
    if pr==1:
        n1=sm+l[i]
        if n1<0:
            sm+=l[i]
            pass 
        else: 
            sm+=l[i]
            req+=sm+1 
            sm=-1 
    else: 
        n1=sm+l[i]
        if n1>0:
            sm+=l[i]
            pass 
        else: 
            sm+=l[i]
            req+=(-sm+1) 
            sm=1 
    pr=1-pr  
req1=0 
pr=0
sm=l[0]
if sm<0:
    pass 
else:
    req1+=sm+1 
for i in range(1,n):
    if pr==1:
        n1=sm+l[i]
        if n1<0:
            sm+=l[i]
            pass 
        else: 
            sm+=l[i]
            req1+=sm+1 
            sm=-1 
    else: 
        n1=sm+l[i]
        if n1>0:
            sm+=l[i]
            pass 
        else: 
            sm+=l[i]
            req1+=(-sm+1) 
            sm=1 
    pr=1-pr  
print(min(req,req1))