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 (3.8.2) (judge verdict: Wrong Answer)

import numpy as np
n = int(input())
a = list(map(int, input().split()))

s = []
ss = a[0]
cnt = 0
c = 1
if(a[0] != 0):
    s.append(a[0])
else:
    while (a[c] == 0):
        c += 1
        cnt += 2
    cnt += 1
    if(np.sign(a[c]) == 1):
        ss = -1
        for i in range(c):
            if(i%2 != c%2):
                s.append(-1)
            else:
                s.append(1)
    else:
        ss = 1
        for i in range(c):
            if(i%2 != c%2):
                s.append(1)
            else:
                s.append(-1)
        
for i in range(c, n):
    ss += a[i]
    if(ss == 0):
        if(np.sign(s[i-1]) == -1):
            ss += 1
            cnt += 1 
            s.append(1)
        else:
            ss -= 1
            cnt += 1
            s.append(-1)
    elif(np.sign(s[i-1]) == np.sign(ss)):
        if(np.sign(s[i-1]) == -1):
            cnt += abs(1 - ss)
            ss = 1
            s.append(1)
        else:
            cnt += abs(-1-ss)
            ss = -1
            s.append(-1)
    else:
        s.append(ss)
print(cnt)