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 T>
int BIT(int i, T s) {
  return (s >> i) & 1;
}
template <class T>
T ONBIT(int i, T s) {
  return s | (T(1) << i);
}
template <class T>
T offbit(T s, int i) {
  return s & (~(T(1) << i));
}
template <class T>
int cntbit(T s) {
  return __builtin_popcount(s);
}
template <class T>
T gcd(T a, T b) {
  T r;
  int dem = 0;
  while (b != 0) {
    r = a % b;
    dem++;
    a = b;
    b = r;
  }
  cout << dem << endl;
  return a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
const int maxv = 500;
const int maxe = maxv * maxv;
const int inf = (int)1e9 + 5;
const long long linf = (long long)1e16 + 5;
const int dr[] = {-1, 0, +1, 0};
const int dc[] = {0, +1, 0, -1};
const long double eps = 1e-9;
const char IN[] = "_.in";
const char OUT[] = "_.out";
const int maxn = 111111;
const int base = 1e9 + 7;
int test;
long long n;
double l, r, m1, m2;
double a[200111], b[200111];
double nick(double x) {
  for (int i = (1); i <= (n); i++) b[i] = a[i] - x;
  double sum = 0.0;
  double res = 0.0;
  double mi = 0, ma = 0;
  for (int i = (1); i <= (n); i++) {
    sum = sum + b[i];
    res = max(res, abs(sum - mi));
    res = max(res, abs(sum - ma));
    mi = min(mi, sum);
    ma = max(ma, sum);
  }
  return res;
}
int smd(int u) {
  int r = 0;
  while (u > 0) {
    r = r + u % 10;
    u = u / 10;
  }
  return r;
}
int main() {
  cin >> n;
  for (int i = (1); i <= (n); i++) cin >> a[i];
  l = -10005;
  r = 10005;
  for (int i = (1); i <= (200); i++) {
    m1 = (l + l + r) / 3;
    m2 = (l + r + r) / 3;
    if (nick(m1) < nick(m2))
      r = m2;
    else
      l = m1;
  }
  cout << fixed << setprecision(7) << nick(l) << endl;
  return 0;
}