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.

Source: codeforces | Difficulty: HARD
Tags: Sorting


Solutions:
def main():
	input()
	a = list(map(int, input().split()))

	def f(a):
		maxend = maxnow = 0
		for x in a:
			maxend = max(0, maxend + x)
			maxnow = max(maxnow, maxend)
		return maxnow
	f1 = lambda x: f((i - x for i in a))
	f2 = lambda x: f((x - i for i in a))
	Max = max((abs(i) for i in a))
	(L, R) = (-Max, Max)
	eps = 10 ** (-8)
	for i in range(100):
		m = (L + R) / 2
		(v1, v2) = (f1(m), f2(m))
		if abs(v1 - v2) < eps:
			break
		if v1 > v2:
			L = m
		else:
			R = m
	print(v1)
main()


def max_sum(nums, shift):
	res = 0
	res_m = 0
	cur_sum = 0
	cur_m_sum = 0
	for i in range(len(nums)):
		cur_sum += nums[i] + shift
		cur_m_sum += nums[i] + shift
		res = max(res, cur_sum)
		cur_sum = max(0, cur_sum)
		res_m = min(res_m, cur_m_sum)
		cur_m_sum = min(0, cur_m_sum)
	return (res, -res_m)

def weaks(nums, shift):
	return max_sum(nums, shift)

def main():
	int(input())
	nums = list(map(int, input().split()))
	l = -10000
	r = 10000
	ans = max(weaks(nums, 0))
	w1 = 1
	w2 = -1
	PREC = 10 ** (-6)
	while abs(w1 - w2) >= PREC and abs(w1 - w2) > PREC * max(w1, w2):
		m = (r + l) / 2
		(w1, w2) = weaks(nums, m)
		if w1 > w2:
			r = m
		else:
			l = m
	print((w1 + w2) / 2)
main()


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

def max_subarray(A):
	max_ending_here = max_so_far = 0
	for x in A:
		max_ending_here = max(0, max_ending_here + x)
		max_so_far = max(max_so_far, max_ending_here)
	return max_so_far

def f1(x):
	return max_subarray((a - x for a in A))

def f2(x):
	return max_subarray((-a + x for a in A))
m = max((abs(a) for a in A))
(l, r) = (-m, m)
for _ in range(100):
	mid = (l + r) / 2
	(v1, v2) = (f1(mid), f2(mid))
	if abs(v1 - v2) < 1e-08:
		break
	elif v1 > v2:
		l = mid
	else:
		r = mid
print(v1)