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 tong(double x, vector<double> a) {
  double maxt = 0, mint = 0, s = 0;
  for (int i = 0; i < a.size(); i++) {
    s += a[i] - x;
    maxt = max(s, maxt);
    mint = min(s, mint);
  }
  return abs(maxt - mint);
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<double> a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  double l = -20000, r = 20000;
  for (int i = 0; i < 100; i++) {
    double l1 = (l + l + r) / 3;
    double r1 = (l + r + r) / 3;
    if (tong(l1, a) > tong(r1, a)) {
      l = l1;
    } else
      r = r1;
  }
  cout << setprecision(6) << fixed << tong(l, a);
  return 0;
}