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:
def cal(x, li, sign):
    sum = 0
    ans = 0
    for i in range(0,n):
        sum += (li[i]-x)*sign
        if sum < 0:
            sum = 0
        if sum > ans:
            ans = sum
    return ans

n = int(input())
li = [int(x) for x in input().split()]

r = max(li)
l = min(li)

ans = -1
mn = 99999999

for i in range(30):
    k = (r+l)/2
    a1 = cal(k, li, 1)
    a2 = cal(k, li, -1)
    if abs(a1) < abs(a2):
        r = k
    else:
        l = k
    if abs(abs(a1)-abs(a2)) < mn:
        mn = abs(abs(a1)-abs(a2))
        ans = abs(a1)
        if abs(a2) > abs(a1):
            ans = abs(a1)
    #print('a1='+str(a1))
    #print('a2='+str(a2))
    if r-l < 1e-6:
        break

print(ans)