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;
int n;
double getMax(double *arr, double x) {
  for (int i = 0; i < n; i++) arr[i] -= x;
  double cur = arr[0], maxm = arr[0];
  bool flag = false;
  for (int i = 0; i < n; i++) {
    if (arr[i] >= 0) {
      flag = true;
    }
    cur = max(arr[i], maxm);
  }
  if (!flag) {
    for (int i = 0; i < n; i++) arr[i] += x;
    return maxm;
  }
  cur = 0, maxm = arr[0];
  for (int i = 0; i < n; i++) {
    cur += arr[i];
    if (cur < 0) cur = 0;
    maxm = max(cur, maxm);
  }
  for (int i = 0; i < n; i++) arr[i] += x;
  return maxm;
}
double getMin(double *arr, double x) {
  for (int i = 0; i < n; i++) arr[i] -= x;
  double cur = arr[0], minm = arr[0];
  bool flag = false;
  for (int i = 0; i < n; i++) {
    if (arr[i] <= 0) {
      flag = true;
    }
    cur = min(cur, minm);
  }
  if (!flag) {
    for (int i = 0; i < n; i++) arr[i] += x;
    return minm;
  }
  cur = 0, minm = arr[0];
  for (int i = 0; i < n; i++) {
    cur += arr[i];
    if (cur > 0) cur = 0;
    minm = min(cur, minm);
  }
  for (int i = 0; i < n; i++) arr[i] += x;
  return minm;
}
double search(double *arr) {
  double lo = *min_element(arr, arr + n);
  double hi = *max_element(arr, arr + n);
  double brr[200200];
  for (int i = 0; i < n; i++) brr[i] = arr[i];
  int t = 200;
  while (t--) {
    double mid = (lo + hi) / 2;
    double maxmp = abs(getMax(brr, mid));
    double maxmn = abs(getMin(brr, mid));
    if (maxmp > maxmn)
      lo = mid;
    else
      hi = mid;
  }
  return (lo + hi) / 2;
}
int main() {
  double arr[200002];
  cin >> n;
  for (int i = 0; i < n; i++) {
    scanf("%lf", &arr[i]);
  }
  double x = search(arr);
  double ans1 = abs(getMax(arr, x));
  double ans2 = abs(getMin(arr, x));
  printf("%.12lf\n", max(ans1, ans2));
  return 0;
}