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, a[200010];
double getf(long double x) {
  double s = 0, Min = 0, Max = 0;
  for (int i = 1; i <= n; i++) {
    s += (double)a[i] - x;
    Min = min(Min, s);
    Max = max(Max, s);
  }
  return Max - Min;
}
int main() {
  scanf("%d", &n);
  int Min = 1000000, Max = -1000000;
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    Min = min(Min, a[i]);
    Max = max(Max, a[i]);
  }
  long double l = Min, r = Max, mid, ma, ml, mr, mb;
  ml = getf(l);
  mr = getf(r);
  while (r - l > 3e-12) {
    mid = (r - l) / 3.0;
    ma = getf(l + mid);
    mb = getf(l + 2 * mid);
    if (ma > mb) {
      ml = ma;
      l = l + mid;
    } else {
      mr = mb;
      r = l + mid + mid;
    }
    if (r - l <= 3e-12) break;
  }
  printf("%.6lf\n", getf(l));
  return 0;
}