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 f(x):
    bi = 0
    ci = 0
    cnt1 = -10 ** 10
    minsum1 = 10 ** 10
    cnt2 = -10 ** 10
    minsum2 = 10 ** 10
    for i in range(len(A)):
        if bi - minsum1 > cnt1:
            cnt1 = bi - minsum1
        if bi <= minsum1:
            minsum1 = bi
        if ci - minsum2 > cnt2:
            cnt2 = ci - minsum2
        if ci <= minsum2:
            minsum2 = ci
        bi += A[i] - x
        ci += x - A[i]
    if bi - minsum1 > cnt1:
        cnt1 = bi - minsum1
    if bi <= minsum1:
        minsum1 = bi
    if ci - minsum2 > cnt2:
        cnt2 = ci - minsum2
    if ci <= minsum2:
        minsum2 = ci
    return max(cnt1, cnt2, 0)


n = int(input())
A = list(map(int, input().split()))
l = min(A)
r = max(A)
for _ in range(70):
    p = l + (r - l) / 3
    q = r - (r - l) / 3
    x = f(p)
    y = f(q)
    if x > y:
        l = p
    elif y > x:
        r = q
    else:
        l = p
        r = q
print(f(l))