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 PYTHON3):

Solution:
n = int(input())
A = list(map(int,input().split()))

def f(A,x,sign=1):
    cur = 0
    mn = 0
    ans = -1<<32
    if sign == 1:
        for y in A:
            cur += y-x
            ans = max(ans, cur - mn)
            mn = min(cur, mn)
    else:
        for y in A:
            cur -= y-x
            ans = max(ans, cur - mn)
            mn = min(cur, mn)

    return ans

lo,hi = -10000,10000
nt = 100
while nt:
    nt -= 1
    mid = (lo+hi)/2
    X = f(A,mid,sign=1)
    Y = f(A,mid,sign=-1)
    if X > Y:
        lo = mid
    else:
        hi = mid
print(abs(f(A,lo)))