Problem: You are given a sequence of n integers a1, a2, ..., an. 

Determine a real number x such that the weakness of the sequence a1 - x, a2 - x, ..., an - x is as small as possible.

The weakness of a sequence is defined as the maximum value of the poorness over all segments (contiguous subsequences) of a sequence.

The poorness of a segment is defined as the absolute value of sum of the elements of segment.

Input

The first line contains one integer n (1 ≤ n ≤ 200 000), the length of a sequence.

The second line contains n integers a1, a2, ..., an (|ai| ≤ 10 000).

Output

Output a real number denoting the minimum possible weakness of a1 - x, a2 - x, ..., an - x. Your answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

3
1 2 3


Output

1.000000000000000


Input

4
1 2 3 4


Output

2.000000000000000


Input

10
1 10 2 9 3 8 4 7 5 6


Output

4.500000000000000

Note

For the first case, the optimal value of x is 2 so the sequence becomes  - 1, 0, 1 and the max poorness occurs at the segment "-1" or segment "1". The poorness value (answer) equals to 1 in this case. 

For the second sample the optimal value of x is 2.5 so the sequence becomes  - 1.5, - 0.5, 0.5, 1.5 and the max poorness occurs on segment "-1.5 -0.5" or "0.5 1.5". The poorness value (answer) equals to 2 in this case.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double poorness(vector<int> v, double x) {
  double total_max = abs(v[0] - x);
  double max_sum = v[0] - x;
  double min_sum = v[0] - x;
  double sum_total_max = max_sum;
  double sum_total_min = min_sum;
  for (int i = 1; i < v.size(); i++) {
    max_sum = max(v[i] - x, v[i] + max_sum - x);
    min_sum = min(v[i] - x, v[i] + min_sum - x);
    sum_total_max = max(sum_total_max, max_sum);
    sum_total_min = min(sum_total_min, min_sum);
    total_max = max(abs(sum_total_max), abs(sum_total_min));
  }
  return total_max;
}
double ternary_search(vector<int> v, double left, double right, int step) {
  if (step == 150) {
    return poorness(v, (right + left) / 2);
  }
  double new_left = left + (right - left) / 3;
  double new_right = new_left + (right - left) / 3;
  if (poorness(v, new_left) < poorness(v, new_right)) {
    return ternary_search(v, left, new_right, step + 1);
  } else {
    return ternary_search(v, new_left, right, step + 1);
  }
}
int main() {
  int n;
  cin >> n;
  vector<int> v(n, 0);
  for (int i = 0; i < n; i++) {
    cin >> v[i];
  }
  cout << fixed << setprecision(15);
  cout << ternary_search(v, -10001, 10001, 0) << endl;
  return 0;
}