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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;

fn main() {
	input!(n: usize);
	input!(a: [i64; n]);

	// 0,2,4・・・が正
	let mut sum: i64 = 0;
	let mut ans: i64 = 0;
	for i in 0..n {
		sum += a[i];
		if i % 2 == 0 {
			if sum <= 0 {
				ans += 1 - sum;
				sum += 1 - sum;
			}
		}
		else {
			if sum >= 0 {
				ans += sum + 1;
				sum -= sum + 1;
			}
		}
	}
//	println!("ans={}", ans);

	// a[0]が負
	let mut sum: i64 = 0;
	let mut ans2: i64 = 0;
	for i in 0..n {
		sum += a[i];
		if i % 2 == 1 {
			if sum <= 0 {
				ans2 += 1 - sum;
				sum += 1 - sum;
			}
		}
		else {
			if sum >= 0 {
				ans2 += sum + 1;
				sum -= sum + 1;
			}
		}
	}
//	println!("ans2={}", ans2);

	println!("{}", std::cmp::min(ans, ans2));
}