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;
double a[1000000];
double b[1000000];
long long int i, j, n;
double k, p, t, m, r, u, z, x, y, l, g, w, q;
double check() {
  long long int i;
  double sum, ans;
  ans = -10;
  sum = 0;
  for (i = 1; i <= n; i++) {
    sum += a[i];
    if (sum < 0) sum = 0;
    if (sum > ans) ans = sum;
  }
  return ans;
}
double check1() {
  long long int i;
  double sum, ans;
  ans = -10;
  sum = 0;
  for (i = 1; i <= n; i++) {
    sum += b[i];
    if (sum < 0) sum = 0;
    if (sum > ans) ans = sum;
  }
  return ans;
}
int main() {
  cin >> n;
  for (i = 1; i <= n; i++) cin >> a[i];
  x = check();
  for (i = 1; i <= n; i++) a[i] *= -1;
  y = check();
  if (x == y) {
    cout << x;
    exit(0);
  }
  if (x < y) {
    swap(x, y);
  } else {
    for (i = 1; i <= n; i++) a[i] *= -1;
  }
  l = 0;
  r = 10001;
  for (j = 1; j <= 100; j++) {
    m = (l + r) / 2;
    for (i = 1; i <= n; i++) {
      b[i] = a[i] - m;
    }
    p = check1();
    for (i = 1; i <= n; i++) {
      b[i] = b[i] * -1;
    }
    q = check1();
    if (p < q)
      r = m;
    else
      l = m;
  }
  std::cout << std::fixed;
  std::cout << std::setprecision(10);
  std::cout << p;
}