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 (2.7.6) (judge verdict: Accepted)

n=input()
a=map(int,raw_input().split())
#print n
#print a

a1_sum=0
a1=[]
for i in a:
	a1_sum+=i
	a1.append(a1_sum)

#print a1


#+,-
b=[]
chn_val=0
for i,val in enumerate(a1):
	val+=chn_val
	if i%2==0:
		if val>0:
			pass
		else:
			t_val=1-val
			chn_val+=t_val
			b.append(t_val)
	else:
		if val<0:
			pass
		else:
			t_val=-1-val
			chn_val+=t_val
			b.append(t_val)
ans1=0
if len(b)==0:
	ans1=0
else:
	for i in b:
		ans1+=abs(i)

#-,+
b=[]
chn_val=0
for i,val in enumerate(a1):
	val+=chn_val
	if i%2==0:
		if val<0:
			pass
		else:
			t_val=-1-val
			chn_val+=t_val
			b.append(t_val)
	else:
		if val>0:
			pass
		else:
			t_val=1-val
			chn_val+=t_val
			b.append(t_val)

ans2=0
if len(b)==0:
	ans2=0
else:
	for i in b:
		ans2+=abs(i)


print min(ans1,ans2)