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 long long N = 2e5 + 10, inf = 1e3 + 5, mod = 1e9 + 7, NN = 1e5 + 10;
int n;
long double a[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> a[i];
  long double low = *min_element(a, a + n), high = *max_element(a, a + n), mid,
              pos = 0, neg = 0;
  for (int temp = 0; temp < 200; temp++) {
    mid = (high + low) / 2;
    long double c = 0;
    pos = neg = 0;
    for (int i = 0; i < n; i++) {
      c += a[i] - mid;
      if (c < 0.0) c = 0;
      pos = max(c, pos);
    }
    c = 0;
    for (int i = 0; i < n; i++) {
      c += mid - a[i];
      if (c < 0.0) c = 0;
      neg = max(neg, c);
    }
    if (pos > neg)
      low = mid;
    else
      high = mid;
  }
  cout << fixed << setprecision(8) << max(pos, neg);
}