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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets.chomp
a = gets.chomp.split(" ").map(&:to_i)

sum_i = 0
sum_i_1 = a[0]
count = 0

for i in 0..n.to_i-2
    sum_i = sum_i + a[i]
    sum_i_1 += a[i + 1]
    #print("sum_i,",sum_i)
    #print("sum_i_1,",sum_i_1)
    if(sum_i == 0)
        sum_i -= a[i]
        a[i] += 1
        sum_i += a[i]
        count += 1
        #print("0でした")
    end
    
    if(sum_i_1 == 0)
        sum_i -= a[i+1]
        if(sum_i > 0)
            a[i+1] -= 1
        elsif (sum_i_1 < 0)
            a[i+1] += 1
        end 
        sum_i += a[i]
        count += 1
        #print("こいつも0でした")
    end

    if ((sum_i > 0) && (sum_i_1 > 0))
        tmp = (-1 - sum_i_1)
        sum_i_1 -= a[i + 1]
        a[i + 1] += tmp
        sum_i_1 += a[i + 1]
        count += tmp.abs
    end
    if((sum_i < 0) && (sum_i_1 < 0))
        tmp = 1 - sum_i_1
        sum_i_1 -= a[i + 1]
        a[i + 1] += tmp
        sum_i_1 += a[i + 1]
        count += tmp.abs
    end
    #print("sum_i,",sum_i)
    #print("sum_i_1,",sum_i_1)

    #print(count)
    #print(a)
    #print("\n")
end

print (count)