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 Go (1.6) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
	"math"
)

func main() {
	var n float64
	fmt.Scan(&n)
	var counter1, counter2 float64 = 0, 0
	var total1, total2 float64 = 0, 0
	var a float64

	for i := 0; i < int(n); i++ {

		fmt.Scan(&a)
		total1 += a
		total2 += a
		if i%2 == 0 {
			if total1 <= 0 {
				counter1 += math.Abs(total1) + 1
				total1 = 1
			}
		} else {
			if total1 >= 0 {
				counter1 += math.Abs(total1) + 1
			}
		}

		if i%2 == 0 {
			if total2 >= 0 {
				counter2 += math.Abs(total2) + 1
				total2 = -1
			}
		} else {
			if total2 <= 0 {
				counter2 += math.Abs(total2) + 1
				total2 = 1
			}
		}
	}

	if counter1 < counter2 {
		fmt.Println(counter1)
	} else {
		fmt.Println(counter2)
	}

}