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;
template <class C>
constexpr int sz(const C &c) {
  return int(c.size());
}
using ll = long long;
using ld = long double;
constexpr const char nl = '\n', sp = ' ';
template <class T, class F, class Cmp = less<T>>
T tsearch(T lo, T hi, F f, int iters, Cmp cmp = less<T>()) {
  for (int it = 0; it < iters; it++) {
    T m1 = lo + (hi - lo) / 3, m2 = hi - (hi - lo) / 3;
    if (cmp(f(m1), f(m2)))
      lo = m1;
    else
      hi = m2;
  }
  return lo + (hi - lo) / 2;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int N;
  cin >> N;
  vector<ld> A(N);
  for (auto &&a : A) cin >> a;
  auto f = [&](ld x) {
    ld ret = 0, cur = 0;
    for (auto &&a : A) {
      cur += a - x;
      if (cur < 0) cur = 0;
      if (ret < cur) ret = cur;
    }
    cur = 0;
    for (auto &&a : A) {
      cur -= a - x;
      if (cur < 0) cur = 0;
      if (ret < cur) ret = cur;
    }
    return ret;
  };
  cout << fixed << setprecision(9)
       << f(tsearch(ld(-3e4), ld(3e4), f, 300, greater<ld>())) << nl;
  return 0;
}