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 main() {
  int n;
  cin >> n;
  vector<double> A(n), B(n);
  for (int i = 0; i < n; i++) {
    cin >> A[i];
    B[i] = A[i];
  }
  double iter = 0, low1 = -20000, high1 = 20000, mid;
  double ans;
  while (iter <= 400) {
    mid = (low1 + high1) / 2;
    for (int i = 0; i < n; i++) B[i] = A[i] - mid;
    double high = 0, prev = 0;
    for (int i = 0; i < n; i++) {
      prev = prev + B[i];
      high = max(high, prev);
      if (prev < 0) prev = 0;
    }
    double low = 0;
    prev = 0;
    for (int i = 0; i < n; i++) {
      prev = prev + B[i];
      low = min(low, prev);
      if (prev > 0) prev = 0;
    }
    ans = high;
    if (high > -low)
      low1 = mid;
    else if (high < -low)
      high1 = mid;
    iter++;
  }
  printf("%.9f\n", ans);
}