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 double e = exp(1.0);
const double INF = 1e9;
const double eps = 1e-11;
double maxX = -INF;
double minX = INF;
const int N = 200000 + 10;
double a[N];
double fx(double v, int n) {
  double tmp = a[0] - v;
  double neg_tmp = a[0] - v;
  bool flag = false;
  if (a[0] < v) flag = true;
  for (int i = 1; i < n; i++) {
    if (a[i] < v) flag = true;
    tmp += a[i] - v;
    if (tmp < a[i] - v) tmp = a[i] - v;
    neg_tmp = max(tmp, neg_tmp);
  }
  if (flag) {
    maxX = v - a[0];
    tmp = v - a[0];
    for (int i = 1; i < n; i++) {
      tmp += v - a[i];
      if (tmp < v - a[i]) tmp = v - a[i];
      maxX = max(tmp, maxX);
    }
  }
  return max(neg_tmp, maxX);
}
int main() {
  int n;
  cin >> n;
  double xi = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    maxX = max(a[i], maxX);
    maxX = max(-a[i], maxX);
    minX = min(a[i], minX);
  }
  double L = -INF;
  double R = INF;
  while (L + eps < R) {
    double mid_L = (2 * L + R) / 3;
    double mid_R = (L + 2 * R) / 3;
    double res_L = fx(mid_L, n);
    double res_R = fx(mid_R, n);
    if (res_L > res_R)
      L = mid_L;
    else
      R = mid_R;
  }
  double answer = (L + R) / 2;
  cout << fixed << setprecision(7) << fx(answer, n);
  return 0;
}