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>
int T;
double a[200005];
double f(double x) {
  int i;
  double m = 0, n = 0, s[200005] = {0};
  for (i = 1; i <= T; i++) {
    s[i] = s[i - 1] + a[i - 1] - x;
    m = m > s[i] ? m : s[i];
    n = n < s[i] ? n : s[i];
  }
  return m - n;
}
int main() {
  int i, t = 200;
  double l = -1e5, m, n, r = 1e5;
  scanf("%d", &T);
  for (i = 0; i < T; i++) scanf("%lf", &a[i]);
  while (t--) {
    m = l + (r - l) / 3;
    n = r - (r - l) / 3;
    if (f(m) < f(n))
      r = n;
    else
      l = m;
  }
  printf("%.15lf\n", f(m));
}