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;
double a[200005];
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%lf", &a[i]);
  double x;
  double low = -10000, high = 10000;
  for (int t = 1; t <= 100; t++) {
    double mid = (low + high) / 2;
    for (int i = 1; i <= n; i++) a[i] -= mid;
    double ans(0), tmp1(0), tmp2(0);
    for (int i = 1; i <= n; i++) {
      ans += a[i];
      if (ans <= 0) ans = 0;
      tmp1 = max(tmp1, ans);
      a[i] = -1.0 * a[i];
    }
    ans = 0;
    for (int i = 1; i <= n; i++) {
      ans += a[i];
      if (ans <= 0) ans = 0;
      tmp2 = max(tmp2, ans);
      a[i] = -a[i];
    }
    if (tmp1 > tmp2)
      low = mid;
    else
      high = mid;
    for (int i = 1; i <= n; i++) a[i] += mid;
  }
  double mid = (low + high) / 2;
  for (int i = 1; i <= n; i++) a[i] -= mid;
  double ans(0), tmp1(0), tmp2(0);
  for (int i = 1; i <= n; i++) {
    ans += a[i];
    if (ans <= 0) ans = 0;
    tmp1 = max(tmp1, ans);
    a[i] = -a[i];
  }
  ans = 0;
  for (int i = 1; i <= n; i++) {
    ans += a[i];
    if (ans <= 0) ans = 0;
    tmp2 = max(tmp2, ans);
  }
  printf("%.15f", max(tmp1, tmp2));
  return 0;
}