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, i;
int mn;
int a[400010];
double mx, sum, l, r, mid, mmid;
double d[400010];
double f(double x) {
  mx = 0;
  for (i = 1; i <= n; i++) d[i] = a[i] - x;
  if (d[1] >= 0)
    sum = d[1];
  else
    sum = 0;
  for (i = 2; i <= n; i++) {
    if (sum - mx > 1e-30) mx = sum;
    if (d[i] + sum >= 0) {
      sum += d[i];
      continue;
    }
    sum = 0;
  }
  if (sum - mx > 1e-30) mx = sum;
  for (i = 1; i <= n; i++) d[i] = x - a[i];
  if (d[1] >= 0)
    sum = d[1];
  else
    sum = 0;
  for (i = 2; i <= n; i++) {
    if (sum - mx > 1e-30) mx = sum;
    if (d[i] + sum >= 0) {
      sum += d[i];
      continue;
    }
    sum = 0;
  }
  if (sum - mx > 1e-30) mx = sum;
  return mx;
}
int main() {
  cin >> n;
  for (i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    mn = max(mn, a[i]);
    mn = max(mn, -a[i]);
  }
  l = -mn;
  r = mn;
  while (l < r - 4e-12) {
    mid = (l + r) / 2;
    mmid = (mid + r) / 2;
    if (f(mid) <= f(mmid))
      r = mmid;
    else
      l = mid;
  }
  printf("%.7f", f(l));
  return 0;
}