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 double eps = 1e-16;
const long long inf = 1000000010;
const int mod = 1000 * 1000 * 1000;
const int MAXN = 1000010;
int n, m, d, x;
long double A[MAXN];
long double calc(long double x) {
  long double mn = 0, mx = 0, tmp = 0;
  for (int i = 0; i < n; i++) {
    tmp += A[i] - x;
    mn = min(mn, tmp);
    mx = max(mx, tmp);
  }
  return mx - mn;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> n;
  for (int i = 0; i < n; i++) cin >> A[i];
  long double l = -inf, r = inf;
  for (int i = 0; i < 200; i++) {
    long double m1 = (2 * l + 1 * r) / 3;
    long double m2 = (1 * l + 2 * r) / 3;
    if (calc(m1) < calc(m2))
      r = m2;
    else
      l = m1;
  }
  cout << setprecision(20) << fixed << calc(l) << endl;
  return 0;
}