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 mn = 200010;
const double inf = 1e18;
int a[mn], n;
double check(double x) {
  double sum = 0, ret = 0, Min = 0, Max = 0;
  for (int i = 1; i <= n; i++) {
    sum += a[i] - x;
    ret = max(ret, fabs(sum - Min));
    ret = max(ret, fabs(sum - Max));
    Min = min(Min, sum);
    Max = max(Max, sum);
  }
  return ret;
}
int main() {
  double l = 0, r;
  int cnt = 0;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    l = min(l, -fabs(a[i]));
  }
  r = -l;
  for (int i = 1; i <= 300; i++) {
    double ml = (r - l) / 3.0 + l, mr = (r - l) / 3.0 * 2.0 + l;
    if (check(ml) < check(mr))
      r = mr;
    else
      l = ml;
  }
  cout << fixed << setprecision(6) << check((l + r) * 0.5);
  return 0;
}