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;
const int maxn = 2e5 + 10;
double a[maxn], b[maxn];
int n;
double mcs() {
  double ans = 0, cur = 0;
  for (int i = 0; i < n; i++) {
    cur += b[i];
    if (cur > ans) ans = cur;
    if (cur < 0) cur = 0;
  }
  return ans;
}
void calc(double mid, double &a1, double &a2) {
  for (int i = 0; i < n; i++) b[i] = a[i] - mid;
  a1 = mcs();
  for (int i = 0; i < n; i++) b[i] = mid - a[i];
  a2 = mcs();
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i < n; i++) scanf("%lf", &a[i]);
  double l = -1e9, r = 1e9, ans = 1e18;
  for (int i = 0; i < 100; i++) {
    double mid = (l + r) / 2, a1, a2;
    calc(mid, a1, a2);
    if (a1 > a2)
      l = mid;
    else
      r = mid;
    ans = min(ans, max(a1, a2));
  }
  printf("%.12f\n", ans);
  return 0;
}