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;
const int MX = 2e5 + 5;
int arr[MX], n;
int inc(double mid) {
  double mxP = 0, mxN = 0, cnt = 0;
  vector<double> temp(n);
  for (int i = 0; i < n; i++) temp[i] = arr[i] * 1.0 - mid;
  for (int i = 0; i < n; i++) {
    if (cnt + temp[i] < 0) {
      cnt = 0;
      continue;
    }
    cnt += temp[i];
    mxP = max(mxP, cnt);
  }
  cnt = 0;
  for (int i = 0; i < n; i++) temp[i] *= -1;
  for (int i = 0; i < n; i++) {
    if (cnt + temp[i] < 0) {
      cnt = 0;
      continue;
    }
    cnt += temp[i];
    mxN = max(mxN, cnt);
  }
  return mxP > mxN;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  double l = -10000, h = 10000, ansP = 0, ansN = 0, ans = 0, anss = 0;
  for (int i = 0; i < 200; i++) {
    double mid = (l + h) / 2;
    if (inc(mid))
      l = mid;
    else
      h = mid;
  }
  double mxP = 0, mxN = 0, cnt = 0;
  vector<double> temp(n);
  for (int i = 0; i < n; i++) temp[i] = arr[i] * 1.0 - h;
  for (int i = 0; i < n; i++) {
    if (cnt + temp[i] < 0) {
      cnt = 0;
      continue;
    }
    cnt += temp[i];
    mxP = max(mxP, cnt);
  }
  cnt = 0;
  for (int i = 0; i < n; i++) temp[i] *= -1;
  for (int i = 0; i < n; i++) {
    if (cnt + temp[i] < 0) {
      cnt = 0;
      continue;
    }
    cnt += temp[i];
    mxN = max(mxN, cnt);
  }
  cout << fixed << setprecision(7);
  cout << max(mxP, mxN) << endl;
  return 0;
}