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;
namespace integer_search {
template <typename Datatype, typename Function>
Datatype first_true(Datatype l, Datatype r, const Datatype not_found,
                    const Function& f) {
  Datatype ans = not_found;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    if (f(m)) {
      ans = m;
      r = m - 1;
    } else {
      l = m + 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype first_false(Datatype l, Datatype r, const Datatype not_found,
                     const Function& f) {
  Datatype ans = not_found;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    if (!f(m)) {
      ans = m;
      r = m - 1;
    } else {
      l = m + 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype last_true(Datatype l, Datatype r, const Datatype not_found,
                   const Function& f) {
  Datatype ans = not_found;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    if (f(m)) {
      ans = m;
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype last_false(Datatype l, Datatype r, const Datatype not_found,
                    const Function& f) {
  Datatype ans = not_found;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    if (!f(m)) {
      ans = m;
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype argmax(Datatype l, Datatype r, const Function& f) {
  Datatype ans = l;
  l += 1;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    if (f(m) > f(m - 1)) {
      ans = m;
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype argmin(Datatype l, Datatype r, const Function& f) {
  Datatype ans = l;
  l += 1;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    if (f(m) < f(m - 1)) {
      ans = m;
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
auto maximum(Datatype l, Datatype r, const Function& f) -> decltype(f(l)) {
  auto ans = f(l);
  l += 1;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    const auto fm = f(m);
    const auto fmm1 = f(m - 1);
    if (fm > fmm1) {
      ans = fm;
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
auto minimum(Datatype l, Datatype r, const Function& f) -> decltype(f(l)) {
  auto ans = f(l);
  l += 1;
  while (l <= r) {
    const Datatype m = l + (r - l) / 2;
    const auto fm = f(m);
    const auto fmm1 = f(m - 1);
    if (fm < fmm1) {
      ans = fm;
      l = m + 1;
    } else {
      r = m - 1;
    }
  }
  return ans;
}
}  // namespace integer_search
namespace floating_search {
template <typename Datatype, typename Function>
Datatype first_true(Datatype l, Datatype r, const Datatype not_found,
                    const int iterations, const Function& f) {
  Datatype ans = not_found;
  for (int iteration = 0; iteration < iterations; ++iteration) {
    const Datatype m = l + (r - l) / 2;
    if (f(m)) {
      ans = m;
      r = m;
    } else {
      l = m;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype first_false(Datatype l, Datatype r, const Datatype not_found,
                     const int iterations, const Function& f) {
  Datatype ans = not_found;
  for (int iteration = 0; iteration < iterations; ++iteration) {
    const Datatype m = l + (r - l) / 2;
    if (!f(m)) {
      ans = m;
      r = m;
    } else {
      l = m;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype last_true(Datatype l, Datatype r, const Datatype not_found,
                   const int iterations, const Function& f) {
  Datatype ans = not_found;
  for (int iteration = 0; iteration < iterations; ++iteration) {
    const Datatype m = l + (r - l) / 2;
    if (f(m)) {
      ans = m;
      l = m;
    } else {
      r = m;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype last_false(Datatype l, Datatype r, const Datatype not_found,
                    const int iterations, const Function& f) {
  Datatype ans = not_found;
  for (int iteration = 0; iteration < iterations; ++iteration) {
    const Datatype m = l + (r - l) / 2;
    if (!f(m)) {
      ans = m;
      l = m;
    } else {
      r = m;
    }
  }
  return ans;
}
template <typename Datatype, typename Function>
Datatype argmax(Datatype l, Datatype r, const int iterations,
                const Function& f) {
  const Datatype golden_ratio = (1 + std::sqrt((Datatype)5)) / 2;
  Datatype m1 = r - (r - l) / golden_ratio;
  Datatype m2 = l + (r - l) / golden_ratio;
  auto fm1 = f(m1);
  auto fm2 = f(m2);
  for (int iteration = 0; iteration < iterations; ++iteration) {
    if (fm1 > fm2) {
      r = m2;
      m2 = m1;
      fm2 = fm1;
      m1 = r - (r - l) / golden_ratio;
      fm1 = f(m1);
    } else {
      l = m1;
      m1 = m2;
      fm1 = fm2;
      m2 = l + (r - l) / golden_ratio;
      fm2 = f(m2);
    }
  }
  return (l + r) / 2;
}
}  // namespace floating_search
int32_t main() {
  int n;
  cin >> n;
  int v[n];
  for (int i = 0; i < n; ++i) cin >> v[i];
  auto f = [&](const double x) {
    double sum1 = 0, sum2 = 0;
    double best = 0;
    for (int i = 0; i < n; ++i) {
      double val = v[i] - x;
      sum1 += val;
      if (sum1 < 0) sum1 = 0;
      sum2 -= val;
      if (sum2 < 0) sum2 = 0;
      best = max(best, sum1);
      best = max(best, sum2);
    }
    return -best;
  };
  double arg = floating_search::argmax(-1e4, 1e4, 500, f);
  double ans = f(arg);
  cout << fixed << setprecision(12) << -ans << endl;
}