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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
implicit none
integer(8) :: i, j, k, nc
integer(8) :: n, sum, sign
integer(8) , allocatable :: a(:)

read(*,*) n
allocate( a(n) )
read(*,*) a

if( a(1) .le. 0 ) then
   sign = -1
else
   sign = 1
end if
sum = a(1)
nc  = 0
do i = 2, n
   sign = sign *(-1)
   if( (sum+a(i))*sign < 0 ) then
      nc = nc+abs(sum+a(i))+1
      a(i) = sign*(abs(sum+a(i))+1) +a(i)
   end if
   sum = sum + a(i)
end do
write(*,'(i0)') nc
end program main