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;
int n;
int A[200000];
double T[200001];
double weakness(double x) {
  T[0] = 0;
  for (int i = 0; i < n; i++) {
    T[i + 1] = T[i] + A[i] - x;
  }
  double mn = T[n], mx = T[n], mxw = 0;
  for (int i = n - 1; i >= 0; i--) {
    mxw = max(mxw, max(abs(mx - T[i]), abs(mn - T[i])));
    if (T[i] > mx) mx = T[i];
    if (T[i] < mn) mn = T[i];
  }
  return mxw;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> A[i];
  int amn = A[0], amx = A[0];
  for (int i = 0; i < n; i++) {
    if (amn > A[i]) amn = A[i];
    if (amx < A[i]) amx = A[i];
  }
  double l = amn, r = amx;
  for (int i = 0; i < 300; i++) {
    double step = (r - l) / 3;
    double m1 = weakness(l + step), m2 = weakness(r - step);
    if (m1 < m2)
      r -= step;
    else
      l += step;
  }
  cout << fixed << setprecision(10) << weakness(l) << "\n";
  return 0;
}