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 weakness(const vector<int> &a, double x) {
  double min = 0, max = 0, sum = 0;
  for (int i = 0, n_ = (a.size()); i < n_; i++) {
    sum += (a[i] - x);
    if (min > sum) min = sum;
    if (max < sum) max = sum;
  }
  return max - min;
}
double fibosearch(const vector<int> &a, double xa, double xb, double xc,
                  double xd, double fa, double fb, double fc, double fd) {
  double change;
  if (fc < fd) {
    change = abs(fb - fd);
    if (change < 1e-7) return (fc + fd) / 2;
    xb = xd;
    fb = fd;
    xd = xc;
    fd = fc;
    xc = xb + 0.61803398875 * (xa - xb);
    fc = weakness(a, xc);
  } else {
    change = abs(fa - fc);
    if (change < 1e-7) return (fc + fd) / 2;
    xa = xc;
    fa = fc;
    xc = xd;
    fc = fd;
    xd = xa + 0.61803398875 * (xb - xa);
    fd = weakness(a, xd);
  }
  return fibosearch(a, xa, xb, xc, xd, fa, fb, fc, fd);
}
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0, n_ = (n); i < n_; i++) cin >> a[i];
  double maxa = a[0], mina = a[0];
  for (int i = 0, n_ = (n); i < n_; i++)
    if (maxa < a[i]) maxa = a[i];
  for (int i = 0, n_ = (n); i < n_; i++)
    if (mina > a[i]) mina = a[i];
  double xa = mina;
  double xb = maxa;
  double xc = xb + 0.61803398875 * (xa - xb);
  double xd = xa + 0.61803398875 * (xb - xa);
  double fa = weakness(a, xa);
  double fb = weakness(a, xb);
  double fc = weakness(a, xc);
  double fd = weakness(a, xd);
  cout << setprecision(9) << fixed
       << fibosearch(a, xa, xb, xc, xd, fa, fb, fc, fd) << endl;
  return 0;
}