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 double pi = acos(-1.0);
const long long mod = 1000000007;
const long long maxn = 200005;
const double epsilon = 1e-11;
double a[maxn], mn, mp;
long long n;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout << setprecision(12) << fixed;
  while (cin >> n) {
    for (int i = 0; i < n; ++i) {
      cin >> a[i];
    }
    long long t = 100;
    double low = *(std::min_element(a, a + n));
    double high = *(std::max_element(a, a + n));
    double mid;
    while (t--) {
      mid = (low + high) / 2.0;
      mn = mod, mp = -mod;
      double cn = 0, cp = 0, tmp;
      for (int i = 0; i < n; ++i) {
        tmp = a[i] - mid;
        cp = max(cp + tmp, tmp);
        cn = min(cn + tmp, tmp);
        mp = max(cp, mp);
        mn = min(cn, mn);
      }
      if (mn + mp > 0) {
        low = mid;
      } else {
        high = mid;
      }
    }
    mn = mod, mp = -mod;
    double cn = 0, cp = 0, tmp;
    for (int i = 0; i < n; ++i) {
      tmp = a[i] - mid;
      cp = max(cp + tmp, tmp);
      cn = min(cn + tmp, tmp);
      mp = max(cp, mp);
      mn = min(cn, mn);
    }
    cout << max(mp, -mn) << "\n";
  }
  return 0;
}