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: Accepted)

n = int(input())
A = list(map(int,input().split()))
B = A[:]
for i in range(1,n):
    B[i] += B[i-1]
C = B[:]
cnt1 = 0
cnt2 = 0
if B[0]<=0:
    cnt1 += abs(1-B[0])
    cnt2 += 1-B[0]
    B[0] += cnt2
for i in range(1,n):
    if i%2==0:
        if B[i]+cnt2<=0:
            cnt1 += abs(1-B[i]-cnt2)
            cnt2 += 1-B[i]-cnt2
            B[i] += cnt2
    else:
        if B[i]+cnt2>=0:
            cnt1 += abs(-1-B[i]-cnt2)
            cnt2 += -1-B[i]-cnt2
            B[i] += cnt2
cnt3 = 0
cnt4 = 0
if C[0]>=0:
    cnt3 += abs(-1-C[0])
    cnt4 += -1-C[0]
    C[0] += cnt4
for i in range(1,n):
    if i%2==0:
        if C[i]+cnt4>=0:
            cnt3 += abs(-1-C[i]-cnt4)
            cnt4 += -1-C[i]-cnt4
            C[i] += cnt4
    else:
        if C[i]+cnt4<=0:
            cnt3 += abs(1-C[i]-cnt4)
            cnt4 += 1-C[i]-cnt4
            C[i] += cnt4
print(min(cnt1,cnt3))