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"
	"math"
	"os"
	"strconv"
)

const pi = math.Pi

var mod int = pow(10, 9) + 7
var Umod uint64 = 1000000007
var ans_1, ans_2 int

func main() {
	reader.Split(bufio.ScanWords)
	n, _ := strconv.Atoi(read())
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i], _ = strconv.Atoi(read())
	}

	sum := make([]int, n)
	sum[0] = a[0]

	if sum[0] != 0 {
		for i := 1; i < n; i++ {
			sum[i] += a[i] + sum[i-1]

			if 0 < sum[i-1] && 0 <= sum[i] {
				// NGパターン
				ans_1 += sum[i] + 1
				sum[i] = -1
			} else if sum[i-1] < 0 && sum[i] <= 0 {
				// NGパターン
				ans_1 += 1 - sum[i]
				sum[i] = 1
			}
		}
		fmt.Println(ans_1)
	} else {
		sum[0], ans_1 = -1, 1
		for i := 1; i < n; i++ {
			sum[i] += a[i] + sum[i-1]

			if 0 < sum[i-1] && 0 <= sum[i] {
				// NGパターン
				ans_1 += sum[i] + 1
				sum[i] = -1
			} else if sum[i-1] < 0 && sum[i] <= 0 {
				// NGパターン
				ans_1 += 1 - sum[i]
				sum[i] = 1
			}
		}

		sum = make([]int, n)
		sum[0], ans_2 = 1, 1
		for i := 1; i < n; i++ {
			sum[i] += a[i] + sum[i-1]

			if 0 < sum[i-1] && 0 <= sum[i] {
				// NGパターン
				ans_2 += sum[i] + 1
				sum[i] = -1
			} else if sum[i-1] < 0 && sum[i] <= 0 {
				// NGパターン
				ans_2 += 1 - sum[i]
				sum[i] = 1
			}
		}
		fmt.Println(min(ans_1, ans_2))
	}
}

/*  ----------------------------------------  */

var reader = bufio.NewScanner(os.Stdin)

func read() string {
	reader.Scan()
	return reader.Text()
}

func lcm(x, y int) int {
	return (x / gcd(x, y)) * y
}

func gcd(x, y int) int {
	if x%y == 0 {
		return y
	} else {
		r := x % y
		return gcd(y, r)
	}
}

var fac [1000000]int
var finv [1000000]int
var inv [1000000]int

func combination_init() {
	fac[0], fac[1] = 1, 1
	finv[0], finv[1] = 1, 1
	inv[1] = 1

	// invは a^(-1) mod p
	// pをaで割ることを考える

	// p/a*(a) + p%a = p
	// p/a*(a) + p%a = 0          (mod p)
	// -p%a = p/a*(a)             (mod p)
	// -p%a *a^(-1)= p/a          (mod p)
	// a^(-1)= p/a * (-p%a)^(-1)  (mod p)
	// a^(-1) =

	for i := 2; i < 1000000; i++ {
		fac[i] = fac[i-1] * i % mod
		inv[i] = mod - inv[mod%i]*(mod/i)%mod
		finv[i] = finv[i-1] * inv[i] % mod
	}
}

func combination(x, y int) int {
	if x < y {
		return 0
	}
	if fac[0] != 1 {
		combination_init()
	}
	return fac[x] * (finv[y] * finv[x-y] % mod) % mod
	//return fac[x] / (fac[y] * fac[x-y])
}

func permutation(x, y int) int {
	if x < y {
		return 0
	}
	if fac[0] != 1 {
		combination_init()
	}
	return fac[x] * (finv[x-y] % mod) % mod
	//return fac[x] / fac[x-y]
}

func max(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Max(float64(x[i]), float64(res)))
	}
	return res
}

func min(x ...int) int {
	var res int = x[0]
	for i := 1; i < len(x); i++ {
		res = int(math.Min(float64(x[i]), float64(res)))
	}
	return res
}
func pow(x, y int) int { return int(math.Pow(float64(x), float64(y))) }
func abs(x int) int    { return int(math.Abs(float64(x))) }
func floor(x int) int  { return int(math.Floor(float64(x))) }
func ceil(x int) int   { return int(math.Ceil(float64(x))) }

type SortBy [][]int

func (a SortBy) Len() int           { return len(a) }
func (a SortBy) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }
func (a SortBy) Less(i, j int) bool { return a[i][0] < a[j][0] }

type PriorityQueue []int

func (h PriorityQueue) Len() int            { return len(h) }
func (h PriorityQueue) Less(i, j int) bool  { return h[i] < h[j] }
func (h PriorityQueue) Swap(i, j int)       { h[i], h[j] = h[j], h[i] }
func (h *PriorityQueue) Push(x interface{}) { *h = append(*h, x.(int)) }
func (h *PriorityQueue) Pop() interface{} {
	old := *h
	n := len(old)
	x := old[n-1]
	*h = old[0 : n-1]
	return x
}