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 = 200005;
const double eps = 1e-12;
const double inf = 1e10;
int n, a[maxn];
double dp[2][maxn];
int main() {
  int i, j;
  scanf("%d", &n);
  for (i = 0; i < n; i++) scanf("%d", &a[i]);
  double t1, t2, mid, lb = -20000, rb = 20000;
  while (rb - lb > eps) {
    mid = (lb + rb) / 2;
    for (i = 0; i < n; i++) dp[0][i] = t1 = -inf, dp[1][i] = t2 = inf;
    for (i = 0; i < n; i++) {
      dp[0][i] = i ? max(a[i] - mid, dp[0][i - 1] + a[i] - mid) : a[i] - mid;
      dp[1][i] = i ? min(a[i] - mid, dp[1][i - 1] + a[i] - mid) : a[i] - mid;
      t1 = max(t1, dp[0][i]);
      t2 = min(t2, dp[1][i]);
    }
    if (t1 + t2 > 0)
      lb = mid;
    else
      rb = mid;
  }
  printf("%.9f\n", t1);
  return 0;
}