You are given a sequence of n integers a_1, a_2, ..., a_{n}. 

Determine a real number x such that the weakness of the sequence a_1 - x, a_2 - x, ..., a_{n} - 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 a_1, a_2, ..., a_{n} (|a_{i}| ≤ 10 000).


-----Output-----

Output a real number denoting the minimum possible weakness of a_1 - x, a_2 - x, ..., a_{n} - 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.

Difficulty: competition

Starter code:

Solutions:
import sys
n = int(sys.stdin.readline())
a = [int(x) for x in sys.stdin.readline().split()]

eps = 1e-12

def f(x):
    mx = a[0] - x
    tsmx = 0.0
    mn = a[0] - x
    tsmn = 0.0
    for ai in a:
        tsmx = max(tsmx + ai - x, ai - x)
        mx = max(tsmx, mx)
        tsmn = min(tsmn + ai - x, ai - x)
        mn = min(tsmn, mn)

    return abs(mx), abs(mn)

l = min(a)
r = max(a)
f1, f2 = f(l)
for i in range(0, 90):
    m = (l + r) / 2
    f1, f2 = f(m)
    if f1 > f2:
        l = m
    else:
        r = m

A, B = f(l)
print(min(A,B))

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))

def weakness(a, x):
    a = [elem-x for elem in a]
    acumulado = maximo = 0
    for elem in a:
        if acumulado + elem > 0:
            acumulado += elem
        else:
            acumulado = 0
        if acumulado > maximo:
            maximo = acumulado
    acumulado = minimo = 0
    for elem in a:
        if acumulado + elem < 0:
            acumulado += elem
        else:
            acumulado = 0
        if acumulado < minimo:
            minimo = acumulado
    return max(maximo, -minimo)


n, a = input(), list(map(int, input().split()))

inf, sup = min(a), max(a)
for _ in range(70):
    c1, c2 = (2*inf+sup)/3, (inf+2*sup)/3
    if weakness(a, c1) < weakness(a, c2):
        sup = c2
    else:
        inf = c1

print(weakness(a, (inf+sup)/2))