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;
inline int Get() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = (x << 1) + (x << 3) + ch - '0';
    ch = getchar();
  }
  return x * f;
}
int n;
double w[200005];
double mx[200005], mn[200005];
double ans = 1e16;
double cal(double x) {
  mx[0] = mn[0] = 0;
  double ans = 0;
  for (int i = 1; i <= n; i++) {
    mx[i] = max(0.0, mx[i - 1]) + w[i] - x;
    mn[i] = min(0.0, mn[i - 1]) + w[i] - x;
    ans = max(ans, max(fabs(mx[i]), fabs(mn[i])));
  }
  return ans;
}
int main() {
  n = Get();
  for (int i = 1; i <= n; i++) {
    scanf("%lf", &w[i]);
  }
  long double l = -10001, r = 10001, mid, rmid;
  while (l + 1e-13 < r) {
    mid = (l + r) / 2;
    rmid = (mid + r) / 2;
    double lx = cal(mid), rx = cal(rmid);
    if (lx + 1e-13 > rx) {
      ans = min(ans, rx);
      l = mid + 1e-13;
    } else {
      ans = min(ans, lx);
      r = rmid - 1e-13;
    }
  }
  printf("%.6lf", ans);
  return 0;
}