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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>

uint64_t solve(int32_t n, const int32_t* a) {
	int32_t i;
	uint64_t cost = 0;
	int64_t value = 0;
	int64_t target = 1;
	for (i = 0; i < n; i++) {
		value += a[i];
		if (value == 0 || (value > 0) != (target > 0)) {
			int64_t diff = value - target;
			if (diff < 0) diff = -diff;
			cost += diff;
			value = target;
		}
		target = -target;
	}
	return cost;
}

int main(void) {
	int32_t n;
	int32_t* a;
	int32_t i;
	uint64_t c1, c2;
	if (scanf("%" SCNd32, &n) != 1) return 1;
	a = malloc(sizeof(*a) * n);
	if (a == NULL) return 2;
	for (i = 0; i < n; i++) {
		if (scanf("%" PRId32, &a[i]) != 1) return 1;
	}
	c1 = solve(n, a);
	for (i = 0; i < n; i++) a[i] = -a[i];
	c2 = solve(n, a);
	printf("%" PRIu64 "\n", c1 <= c2 ? c1 : c2);
	free(a);
	return 0;
}