Problem: You are given two rectangles on a plane. The centers of both rectangles are located in the origin of coordinates (meaning the center of the rectangle's symmetry). The first rectangle's sides are parallel to the coordinate axes: the length of the side that is parallel to the Ox axis, equals w, the length of the side that is parallel to the Oy axis, equals h. The second rectangle can be obtained by rotating the first rectangle relative to the origin of coordinates by angle α.

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Your task is to find the area of the region which belongs to both given rectangles. This region is shaded in the picture.

Input

The first line contains three integers w, h, α (1 ≤ w, h ≤ 106; 0 ≤ α ≤ 180). Angle α is given in degrees.

Output

In a single line print a real number — the area of the region which belongs to both given rectangles.

The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 6.

Examples

Input

1 1 45


Output

0.828427125


Input

6 4 30


Output

19.668384925

Note

The second sample has been drawn on the picture above.

Solution (in PYTHON3):

Solution:
import math
from decimal import *
getcontext().prec = 40

EPS = Decimal(0.000000000000000000001)
PI = Decimal(3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328)

def labs(x):
	if x < 0:
		return -x
	return x

class Point:
	def __init__(self, x, y):
		self.x = x
		self.y = y
	
	def Add(self, p):
		self.x += p.x
		self.y += p.y
	
	def Sub(self, p):
		self.x -= p.x
		self.y -= p.y

	def Scale(self, v):
		self.x *= v
		self.y *= v

	def Rotate(self, angle):
		newX = self.x * Decimal(math.cos(angle)) - self.y * Decimal(math.sin(angle))
		newY = self.x * Decimal(math.sin(angle)) + self.y * Decimal(math.cos(angle))
		self.x = newX
		self.y = newY
	
	def Equals(self, p):
		if Decimal(labs(p.x - self.x)) < EPS and Decimal(labs(p.y - self.y)) < EPS:
			return True
		return False

class Line:
	def __init__(self, start, end):
		self.start = start
		self.end = end
	
	def GetIntersection(self, l):
		a = Point(self.start.x, self.start.y)
		b = Point(self.end.x, self.end.y)
		c = Point(l.start.x, l.start.y)
		d = Point(l.end.x, l.end.y)
		ab = Point(self.end.x, self.end.y)
		cd = Point(l.end.x, l.end.y)
		ab.Sub(a)
		cd.Sub(c)
		k = Decimal((cd.x * (a.y - c.y) + cd.y * (c.x - a.x)) / (ab.x * cd.y - ab.y * cd.x))
		ab.Scale(k)
		a.Add(ab)
		return a

class Polygon:
	def __init__(self, vertices):
		self.vertices = vertices

	def GetArea(self): 
		area = Decimal(0)
		for i in range(0, len(self.vertices)):
			area += self.vertices[i].x * self.vertices[(i + 1) % len(self.vertices)].y - self.vertices[(i + 1) % len(self.vertices)].x * self.vertices[i].y
		return Decimal(labs(area)) / Decimal(2)

x, y, alpha = input().split()
x = Decimal(x)
y = Decimal(y)
if x < y:
	tmp = x
	x = y
	y = tmp
alpha = Decimal(alpha)
singleArea = x * y
if alpha > 90:
	alpha = Decimal(180) - alpha
if alpha == 0:
	print(singleArea)
	exit()
alpha = alpha * PI / Decimal(180)
a = Point(x / Decimal(2), y / Decimal(2))
b = Point(x / Decimal(2), -y / Decimal(2))
c = Point(-x / Decimal(2), -y / Decimal(2))
d = Point(-x / Decimal(2), y / Decimal(2))
e = Point(a.x, a.y)
f = Point(b.x, b.y)
g = Point(c.x, c.y)
h = Point(d.x, d.y)
e.Rotate(alpha)
f.Rotate(alpha)
g.Rotate(alpha)
h.Rotate(alpha)
ab = Line(a, b)
bc = Line(b, c)
cd = Line(c, d)
da = Line(d, a)
ef = Line(e, f)
fg = Line(f, g)
gh = Line(g, h)
he = Line(h, e)
area = 0
if a.Equals(f):
	t1 = Polygon([he.GetIntersection(da), e, f])
	t2 = Polygon([fg.GetIntersection(bc), g, h])
	area = singleArea - t1.GetArea() - t2.GetArea()
elif f.y > a.y:
	p1 = Polygon([he.GetIntersection(da), e, f, fg.GetIntersection(da)])
	p2 = Polygon([fg.GetIntersection(bc), g, h, he.GetIntersection(bc)])
	area = singleArea - p1.GetArea() - p2.GetArea()
else:
	t1 = Polygon([da.GetIntersection(he), e, ef.GetIntersection(da)])
	t2 = Polygon([ef.GetIntersection(ab), f, fg.GetIntersection(ab)])
	t3 = Polygon([fg.GetIntersection(bc), g, gh.GetIntersection(bc)])
	t4 = Polygon([gh.GetIntersection(cd), h, he.GetIntersection(cd)])
	area = singleArea - t1.GetArea() - t2.GetArea() - t3.GetArea() - t4.GetArea()
print(area)