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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func Scanner() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	buf := make([]byte, 0)
	sc.Buffer(buf, 1000000009)
	sc.Split(bufio.ScanWords)
	n, _ := strconv.Atoi(Scanner())
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i], _ = strconv.Atoi(Scanner())
	}
	s := a[0]
	ans := 0
	if s == 0 && a[1] > 0 {
		s = -1
		ans += 1
	} else if s == 0 && a[1] < 0 {
		s = 1
		ans += 1
	}
	for i := 1; i < n; i++ {
		t := s + a[i]
		if s < 0 && t < 0 {
			ans += 1 - t
			s = 1
		} else if s > 0 && t > 0 {
			ans += t + 1
			s = -1
		} else if s < 0 && t == 0 {
			ans += 1
			s = 1
		} else if s > 0 && t == 0 {
			ans += 1
			s = -1
		} else {
			s = t
		}
	}
	fmt.Println(ans)
}