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;
int n;
int a[200005];
double check(double mid) {
  double ans = 0.0;
  double x = 0.0, y = 0.0;
  double hamada = 0.0;
  for (int i = 0; i < n; i++) {
    hamada += a[i] - mid;
    ans = max(ans, max(fabs(hamada - x), fabs(hamada - y)));
    x = max(x, hamada);
    y = min(y, hamada);
  }
  return ans;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) scanf("%d", &a[i]);
  double lo = -10000.0, hi = 10000.0;
  int x = 0;
  while (x++ < 500) {
    double mid1 = (lo + lo + hi) / 3.0, mid2 = (hi + hi + lo) / 3.0;
    if (check(mid1) > check(mid2)) {
      lo = mid1;
    } else
      hi = mid2;
  }
  printf("%.12lf", check((lo + hi) / 2.0));
  return 0;
}