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 arr[200005], temp[200005], dp[200005];
double x;
double minuss, pluss;
void check(double x) {
  minuss = 10000.0, pluss = -10000.0;
  for (int i = 1; i <= n; i++) dp[i] = 0.0;
  for (int i = 1; i <= n; i++) temp[i] = arr[i] - x;
  for (int i = 1; i <= n; i++) dp[i] = max(temp[i], dp[i - 1] + temp[i]);
  for (int i = 1; i <= n; i++) pluss = max(pluss, dp[i]);
  for (int i = 1; i <= n; i++) dp[i] = 0.0;
  for (int i = 1; i <= n; i++) dp[i] = min(temp[i], dp[i - 1] + temp[i]);
  for (int i = 1; i <= n; i++) minuss = min(minuss, dp[i]);
  minuss = abs(minuss);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) scanf("%lf", &arr[i]);
  cout.precision(10);
  double l = -10000.0;
  double r = 10000.0;
  int cnt = 0;
  while (l <= r && cnt < 100) {
    double mid = (l + r) / 2.0;
    check(mid);
    if (pluss > minuss)
      l = mid;
    else if (minuss > pluss)
      r = mid;
    else
      break;
    cnt++;
  }
  cout << max(minuss, pluss) << endl;
  return 0;
}