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;
long double a[200100], b[200100];
int n;
long double tru(long double x) {
  int k;
  long double max = 0, pos = 0, neg = 0;
  for (k = 1; k <= n; k++) {
    b[k] = a[k] + x;
  }
  for (k = 1; k <= n; k++) {
    pos += b[k];
    neg += b[k];
    if (fabs(pos) > max) max = fabs(pos);
    if (fabs(neg) > max) max = fabs(neg);
    if (pos < 0) pos = 0;
    if (neg > 0) neg = 0;
  }
  return max;
}
int main() {
  int k;
  cin >> n;
  long double d = 1e-12, l = -123034, r = 171022, p, q, m;
  for (k = 1; k <= n; k++) cin >> a[k];
  for (k = 1; k <= 100; k++) {
    m = (l + r) / 2;
    p = tru(m);
    q = tru(m + d);
    if (p > q)
      l = m;
    else
      r = m;
  }
  cout << setprecision(12) << tru(m);
}