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 = 200100;
const long double inf = 1e15;
const long double eps = 1e-15;
int n, a[maxn];
long double dabs(long double d) {
  if (d < 0)
    return d * -1;
  else
    return d;
}
long double go(long double k) {
  long double mi = 0, ma = 0, cur = 0;
  long double ans = 0;
  for (int i = 0; i < n; i++) {
    cur += a[i] - k;
    ans = max(ans, max(dabs(cur - mi), dabs(cur - ma)));
    mi = min(mi, cur);
    ma = max(ma, cur);
  }
  return ans;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  long double lo = -10005, hi = 10005;
  while (hi - lo > eps) {
    long double m1 = lo + (hi - lo) / 3, m2 = lo + 2 * (hi - lo) / 3;
    if (go(m1) < go(m2))
      hi = m2;
    else
      lo = m1;
  }
  cout << fixed << setprecision(10) << go(lo) << '\n';
}