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 n, a[200005], sum[200005];
const double EPS = 0.000000000005;
double f(double x) {
  double ans = -999999999, t_sum = 0, max_sum = -999999999, min_sum = 999999999,
         temp;
  for (int i = 0; i < n; i++) {
    t_sum += a[i] - x;
    sum[i] = t_sum;
  }
  for (int i = 0; i < n; i++) {
    ans = max(ans, abs(sum[i]));
    if (i != 0) {
      if (sum[i] < 0) {
        temp = sum[i] - max_sum;
        ans = max(ans, abs(temp));
      } else {
        temp = sum[i] - min_sum;
        ans = max(ans, abs(temp));
      }
    }
    if (sum[i] > max_sum) {
      max_sum = sum[i];
    }
    if (sum[i] < min_sum) {
      min_sum = sum[i];
    }
  }
  return ans;
}
double solve() {
  double l = -10000, r = 10000, m1, m2;
  while (r - l > EPS) {
    m1 = l + (r - l) / 3;
    m2 = r - (r - l) / 3;
    if (f(m1) < f(m2)) {
      r = m2;
    } else {
      l = m1;
    }
  }
  return r;
}
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  cout << fixed << setprecision(7) << f(solve());
  return 0;
}