You are given a convex polygon P with n distinct vertices p1, p2, ..., pn. Vertex pi has coordinates (xi, yi) in the 2D plane. These vertices are listed in clockwise order.

You can choose a real number D and move each vertex of the polygon a distance of at most D from their original positions.

Find the maximum value of D such that no matter how you move the vertices, the polygon does not intersect itself and stays convex.

Input

The first line has one integer n (4 ≤ n ≤ 1 000) — the number of vertices.

The next n lines contain the coordinates of the vertices. Line i contains two integers xi and yi ( - 109 ≤ xi, yi ≤ 109) — the coordinates of the i-th vertex. These points are guaranteed to be given in clockwise order, and will form a strictly convex polygon (in particular, no three consecutive points lie on the same straight line).

Output

Print one real number D, which is the maximum real number such that no matter how you move the vertices, the polygon stays convex.

Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely, let's assume that your answer is a and the answer of the jury is b. The checker program will consider your answer correct if <image>.

Examples

Input

4
0 0
0 1
1 1
1 0


Output

0.3535533906


Input

6
5 0
10 0
12 -4
10 -8
5 -8
3 -4


Output

1.0000000000

Note

Here is a picture of the first sample

<image>

Here is an example of making the polygon non-convex.

<image>

This is not an optimal solution, since the maximum distance we moved one point is  ≈ 0.4242640687, whereas we can make it non-convex by only moving each point a distance of at most  ≈ 0.3535533906.

Difficulty: MEDIUM_HARD
Tags: Geometry

Starter code:

Solutions:
from collections import Counter
n = int(input())
a = []
for i in range(n):
	a.append(list(map(int, input().split())))
m = 10000000000
for i in range(-1, n - 1):
	b = a[i + 1][0] - a[i - 1][0]
	c = a[i - 1][1] - a[i + 1][1]
	d = -a[i - 1][1] * b - a[i - 1][0] * c
	m = min(m, ((a[i - 1][0] - a[i][0]) ** 2 + (a[i - 1][1] - a[i][1]) ** 2) ** 0.5, ((a[i + 1][0] - a[i][0]) ** 2 + (a[i + 1][1] - a[i][1]) ** 2) ** 0.5, abs(b * a[i][1] + c * a[i][0] + d) / (b ** 2 + c ** 2) ** 0.5)
print(m / 2)


def r(pred, cur, nxt):
	(x1, y1) = (nxt['x'] - pred['x'], nxt['y'] - pred['y'])
	(x2, y2) = (cur['x'] - pred['x'], cur['y'] - pred['y'])
	m = abs(x1 * y2 - x2 * y1)
	return m / (x1 ** 2 + y1 ** 2) ** 0.5
n = int(input())
a = []
for i in range(n):
	(x, y) = (int(_) for _ in input().split())
	a.append({'x': x, 'y': y})
min_r = r(a[-1], a[0], a[1]) / 2
for i in range(1, n):
	min_r = min(min_r, r(a[i - 1], a[i], a[(i + 1) % n]) / 2)
print(min_r)


n = int(input())
P = []

def h(p1, p2, m):
	return abs(((p2[0] - p1[0]) * (m[1] - p1[1]) - (p2[1] - p1[1]) * (m[0] - p1[0])) / ((p2[0] - p1[0]) ** 2 + (p2[1] - p1[1]) ** 2) ** 0.5)
for i in range(n):
	P.append(list(map(int, input().split())))
answer = float('inf')
for i in range(n):
	cw = P[(i + 1) % n]
	ucw = P[i - 1]
	answer = min(answer, h(cw, ucw, P[i]) / 2)
print(answer)


import sys, queue, string, math
try:
	import dev_act_ffc429465ab634
	DEV = True
except:
	DEV = False

def log(*s):
	if DEV:
		print('LOG', *s)

class EJudge:

	def __init__(self, problem='default', reclim=1 << 30):
		self.problem = problem
		sys.setrecursionlimit(reclim)

	def use_files(self, infile='', outfile=''):
		if infile != '':
			self.infile = open(infile)
			sys.stdin = self.infile
		if infile != '':
			self.outfile = open(outfile, 'w')
			sys.stdout = self.outfile

	def use_bacs_files(self):
		self.use_files(self.problem + '.in', self.problem + '.out')

	def get_tl(self):
		while True:
			pass

	def get_ml(self):
		tmp = [[[5] * 100000 for _ in range(1000)]]
		while True:
			tmp.append([[5] * 100000 for _ in range(1000)])

	def get_re(self):
		s = (0,)[8]

	def get_wa(self, wstr='blablalblah'):
		for _ in range(3):
			print(wstr)
		exit()

class IntReader:

	def __init__(self):
		self.ost = queue.Queue()

	def get(self):
		return int(self.sget())

	def sget(self):
		if self.ost.empty():
			for el in input().split():
				self.ost.put(el)
		return self.ost.get()

	def release(self):
		res = []
		while not self.ost.empty():
			res.append(self.ost.get())
		return res

def tokenized(s):
	word = []
	for ch in s.strip():
		if ch == ' ':
			if word:
				yield ''.join(word)
				word = []
		elif 'a' <= ch <= 'z' or 'A' <= ch <= 'Z' or '0' <= ch <= '9':
			word.append(ch)
		else:
			if word:
				yield ''.join(word)
				word = []
			yield ch
	if word:
		yield ''.join(word)
		word = []
ej = EJudge()
int_reader = IntReader()
fmap = lambda f, *l: list(map(f, *l))
parse_int = lambda : fmap(int, input().split())

def dist(a, b):
	return math.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2)

def geron(la, lb, lc):
	halfp = (la + lb + lc) / 2
	return math.sqrt(halfp * (halfp - la) * (halfp - lb) * (halfp - lc))

def oriented(a, b, c):
	return abs((b[0] - a[0]) * (c[1] - a[1]) - (b[1] - a[1]) * (c[0] - a[0])) / 2

def add_tria_desec(a, b, c):
	global ans
	(la, lb, lc) = (dist(b, c), dist(c, a), dist(a, b))
	s = oriented(a, b, c)
	h = s * 2 / lb
	dmax = h / 2
	ans = min(ans, dmax)
n = int(input())
points = [parse_int() for _ in range(n)]
ans = 1 << 32
for idx in range(-2, n - 2):
	log(idx, idx + 1, idx + 2)
	add_tria_desec(points[idx], points[idx + 1], points[idx + 2])
print(ans)


from sys import stdin, stdout
import math
n = int(stdin.readline().rstrip())
pointsList = []
for i in range(n):
	(x, y) = map(int, stdin.readline().rstrip().split())
	pointsList.append((x, y))
maxD = 999999999999999
for i in range(n):
	if i == n - 2:
		j = n - 1
		k = 0
	elif i == n - 1:
		j = 0
		k = 1
	else:
		j = i + 1
		k = i + 2
	(p1x, p1y) = pointsList[i]
	(p3x, p3y) = pointsList[k]
	p3x -= p1x
	p3y -= p1y
	theta = math.atan2(p3y, p3x)
	(p2x, p2y) = pointsList[j]
	p2x -= p1x
	p2y -= p1y
	y = -p2x * math.sin(theta) + p2y * math.cos(theta)
	maxD = min(y / 2, maxD)
print(maxD)


def calc(distance_1, distance_2, distance_3):
	return ((2 * distance_1 * distance_3 + 2 * distance_2 * distance_3 - distance_3 * distance_3 - (distance_1 - distance_2) ** 2) / (16 * distance_3)) ** 0.5

def distance(point_1, point_2):
	(point_1, y1) = point_1
	(point_2, y2) = point_2
	return (point_1 - point_2) ** 2 + (y1 - y2) ** 2
n = int(input().strip())
points = []
for _ in range(n):
	points.append(tuple([int(x) for x in input().strip().split()]))
min_ = float('inf')
for i in range(n):
	distance_1 = distance(points[i], points[(i + 1) % n])
	distance_2 = distance(points[(i + 2) % n], points[(i + 1) % n])
	distance_3 = distance(points[(i + 2) % n], points[i])
	min_ = min(min_, calc(distance_1, distance_2, distance_3))
print('%.9f' % min_)


d = lambda i, j: (t[i][0] - t[j % n][0]) ** 2 + (t[i][1] - t[j % n][1]) ** 2
n = int(input())
t = [list(map(int, input().split())) for q in range(n)]
h = 1e+20
for i in range(n):
	(a, b, c) = (d(i - 1, i), d(i, i + 1), d(i - 1, i + 1))
	h = min(h, (4 * a * b - (a + b - c) ** 2) / c)
print(h ** 0.5 / 4)


def d(x, y, x1, y1, x2, y2):
	if x1 == x2:
		return abs(x - x1)
	elif y1 == y2:
		return abs(y - y1)
	else:
		return abs(((x - x1) / (x2 - x1) - (y - y1) / (y2 - y1)) / (1 / (x2 - x1) ** 2 + 1 / (y2 - y1) ** 2) ** 0.5)

def delta(a, b, c):
	return d(a[0], a[1], b[0], b[1], c[0], c[1]) / 2
n = int(input())
data = [list(map(int, input().split())) for t in range(n)]
data.append(data[0])
data.append(data[1])
print(min(map(delta, data[1:], data, data[2:])))