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[200009];
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  double l, r, mid;
  double maxpos, maxneg, tmpp, tmpn, ta;
  int i;
  l = -100001;
  r = 100001;
  int deepness = 0;
  while (fabs(r - l) > 0.0000000000001) {
    deepness++;
    mid = (l + r) / 2.0;
    maxpos = 0.000000000000;
    maxneg = 0.000000000000;
    tmpp = 0.000000000000;
    tmpn = 0.000000000000;
    for (i = 1; i <= n; i++) {
      ta = a[i] - mid;
      tmpp += ta;
      tmpn += -ta;
      maxpos = max(tmpp, maxpos);
      maxneg = max(tmpn, maxneg);
      tmpp = max(tmpp, 0.0000000000);
      tmpn = max(tmpn, 0.0000000000);
    }
    if (maxpos > maxneg) {
      l = mid;
    } else {
      r = mid;
    }
    if (deepness >= 100) break;
  }
  printf("%.10lf", max(maxpos, maxneg));
}