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;
const int MAXN = 200000;
double a[MAXN];
int N;
bool increasing(double x, double& maxsum) {
  double last_maxp, last_maxn, maxp, maxn;
  last_maxp = last_maxn = maxp = maxn = 1e-18;
  for (int i = 0; i <= N - 1; ++i) {
    last_maxp = max(last_maxp + a[i] - x, a[i] - x);
    maxp = max(maxp, last_maxp);
    last_maxn = max(last_maxn + x - a[i], x - a[i]);
    maxn = max(maxn, last_maxn);
  }
  maxsum = max(maxn, maxp);
  return maxn > maxp;
}
int main() {
  cin >> N;
  for (int i = 0; i <= N - 1; ++i) cin >> a[i];
  double l = -1e4, r = 1e4;
  double ans;
  for (int _ = 1; _ <= 100; ++_) {
    double m = (l + r) * 0.5;
    if (increasing(m, ans))
      r = m;
    else
      l = m;
  }
  cout << setprecision(20) << fixed << ans << '\n';
  return 0;
}