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 N = 200005;
int a[N], n;
double poorness(double x) {
  double csp = 0, bs = 0, csn = 0;
  for (int i = 0; i < n; i++) {
    csp += (double)a[i] - x;
    csn += (double)a[i] - x;
    if (csp < 0) csp = 0;
    if (csn > 0) csn = 0;
    bs = max(bs, csp);
    bs = max(bs, -csn);
  }
  return bs;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  double l = -10000.0, r = 10000.0, ans = 1e10;
  int t = 400;
  while (t--) {
    double m1 = l + (r - l) / 3.0, m2 = r - (r - l) / 3.0;
    double fm1 = poorness(m1), fm2 = poorness(m2);
    if (fm1 > fm2)
      l = m1;
    else
      r = m2;
    ans = min(ans, fm1);
    ans = min(ans, fm2);
  }
  cout << fixed << setprecision(10) << ans;
}