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: Wrong Answer)

import sys
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
sys.setrecursionlimit(10 ** 7)

n = int(readline())
a = list(map(int, readline().split()))
if a[0] > 0:
    cnt2 = a[0] + 1
    now2 = -1
    cnt1 = 0
    now1 = a[0]
else:
    cnt2 = 0
    now2 = a[0]
    cnt1 = -a[0] + 1
    now1 = 1

for i, aa in enumerate(a[1:]):
    if i % 2 == 0:
        if aa + now2 > 0:
            now2 += aa
        else:
            cnt2 += abs(now2 + aa) + 1
            now2 = 1
        if now1 + aa < 0:
            now1 += aa
        else:
            cnt1 += now1 + aa + 1
            now1 = -1
    else:
        if aa + now1 > 0:
            now1 += aa
        else:
            cnt1 += abs(now1 + aa) + 1
            now1 = 1
        if now2 + aa < 0:
            now2 += aa
        else:
            cnt2 += now2 + aa + 1
            now2 = -1
print(min(cnt1, cnt2))