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: Runtime Error)

import sys
input=sys.stdin.readline
input = open(sys.argv[1], "r").readline

def main():
    N = int(input())
    A = list(map(int, input().split()))
    tmp = A.copy()
    mi = -1
    for j in range(2):
        A = tmp.copy()
        s = 0
        n = 0
        if j == 0: # 偶数番目までの和が正 ⇒ A[0] を負にする
            if A[0] > 0:
                n += abs(A[0] +1)
                A[0] = -1
        else:   # 奇数番目までの和が正 ⇒ A[0] を正にする
            if A[0] < 0:
                n += abs(A[0] -1)
                A[0] = 1
        s = A[0]
#        print(A)
        for i in range(1,N):
            if s * (s+A[i]) >= 0:
                if s < 0:
                    n += abs(-s+1 -A[i])
                    A[i] = -s+1
                else:
                    n += abs(-s-1 -A[i])
                    A[i] = -s-1
            s += A[i]
        if mi == -1:
            mi = n
        else:
            mi = min(mi, n)
    print(mi)

if __name__ == '__main__':
    main()