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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(s) {
  var s = s.split("\n");
  var n = parseInt(s[0], 10);
  var a = s[1].split(" ").map(e => parseInt(e, 10));
  var acc = 0, cnt = 0, arr = [];
  for (var i = 0; i < n; i++) {
    acc += a[i];
    if (i === 0) {
      if (acc === 0) {
        if (a[i + 1] >= 0) {
          acc -= (a[i + 1] - 1);
          if (acc === 0) acc--;
          cnt += Math.abs(acc);
        } else {
          acc += (Math.abs(a[i + 1]) - 1);
          if (acc === 0) acc++;
          cnt += acc;
        }
      }
    } else {
      if (arr[i - 1] > 0) {
        if (acc >= 0) {
          cnt += (acc + 1);
          acc -= (acc + 1);
        }
      } else {
        if (acc <= 0) {
          cnt += (Math.abs(acc) + 1);
          acc += (Math.abs(acc) + 1);
        }
      }
    }
    arr.push(acc);
  }
  console.log(cnt);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));