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 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
		# print (w1,w2,r,l,m)
		w1, w2 = weaks(nums, m)
		# print(w1, w2)
		if w1 > w2:
			r = m
		else: 
			l = m
	print ((w1 + w2) / 2)

# print (weaks([1,2,3],-2500.0))
main()