IT City administration has no rest because of the fame of the Pyramids in Egypt. There is a project of construction of pyramid complex near the city in the place called Emerald Walley. The distinction of the complex is that its pyramids will be not only quadrangular as in Egypt but also triangular and pentagonal. Of course the amount of the city budget funds for the construction depends on the pyramids' volume. Your task is to calculate the volume of the pilot project consisting of three pyramids — one triangular, one quadrangular and one pentagonal.

The first pyramid has equilateral triangle as its base, and all 6 edges of the pyramid have equal length. The second pyramid has a square as its base and all 8 edges of the pyramid have equal length. The third pyramid has a regular pentagon as its base and all 10 edges of the pyramid have equal length. [Image] 


-----Input-----

The only line of the input contains three integers l_3, l_4, l_5 (1 ≤ l_3, l_4, l_5 ≤ 1000) — the edge lengths of triangular, quadrangular and pentagonal pyramids correspondingly.


-----Output-----

Output one number — the total volume of the pyramids. Absolute or relative error should not be greater than 10^{ - 9}.


-----Examples-----
Input
2 5 3

Output
38.546168065709

Difficulty: interview

Starter code:

Solutions:
from math import sqrt

a, b, c = list(map(int, input().split()))
# a, b, c = 2, 5, 3

V1 = a ** 3 * sqrt(2) / 12
V2 = sqrt(2) * (b ** 3) / 6
V3 = ((5 + sqrt(5)) / 24) * (c ** 3)

print(V1 + V2 + V3)


__author__ = 'panag'
import sys
import math

l1, l2, l3 = map(int, sys.stdin.readline().split(' '))

#print(l1, l2, l3)
#1


v1 = ((math.sqrt(3)/4*l1**2) * 1/3 * (math.sqrt(l1**2 - (math.sqrt(3)/3*l1)**2))) + (l2 ** 2 * 1/3 * (math.sqrt(l2**2 - (l2/math.sqrt(2))**2))) + (((math.sqrt(5)*math.sqrt(5+2*math.sqrt(5)))/4 * l3**2) * 1/3 * (math.sqrt(l3**2 - ((math.sqrt(10)*math.sqrt(5+math.sqrt(5)))/10 * l3)**2)))

print(v1)

from math import sin, cos, pi, tan

l3, l4, l5 = map(int, input().split())

def f(n, x):
    R = 0.5 * x / sin(pi / n)
    h = (x**2 - R**2)**0.5
    base = n * R**2 * sin(2 * pi / n) * 0.5
    return base * h / 3


print(f(3, l3) + f(4,l4) + f(5,l5))

a, b, c = list(map(int, input().split()))
ans = (a ** 3 * 2 ** 0.5) / 12
ans += (b ** 3 * 2 ** 0.5) / 6
R = 10 ** 0.5 / 10 * (5 + 5 ** 0.5) ** 0.5 * c
X = (c ** 2 - R ** 2) ** 0.5
s = c ** 2 * (25 + 10 * 5 ** 0.5) ** 0.5 / 4
ans += X * s / 3
print(ans)

l3,l4,l5=list(map(int,input().split()))
V3=2**0.5/12*l3**3
V4=2**0.5/6*l4**3
V5=0.3015028323958315*l5**3
print(V3+V4+V5)


from functools import reduce
from math import factorial
l1, l2, l3 = [int(x) for x in input().split()]
A = (2**0.5)/12
B = ((15 + 5*5**0.5)/288)**0.5
print((l1**3 + 2*l2**3)*A + B*l3**3)



from decimal import *
from math import sqrt,tan,pi

def __starting_point():

    getcontext().prec = 50

    l3,l4,l5 = map( Decimal , input().split() )
    #print(l3,l4,l5)

    S3 = Decimal(sqrt(3))*l3*l3/4
    H3 = Decimal(sqrt(6))*l3/3
    area3 = S3*H3/3

    S4 = l4*l4
    H4 = Decimal(sqrt(2))*l4/2
    area4 = S4*H4/3

    h5 = l5*Decimal(tan(54*pi/180))/2
    S5 = (l5*h5/2)*5
    H5 = Decimal(sqrt((3*l5*l5/4)-(h5*h5)))
    area5 = S5*H5/3

    res = area3 + area4 + area5

    print(res)
__starting_point()

l3, l4, l5 = map(int, input().split())
v3 = l3 ** 3 / (6 * 2 ** 0.5)
v4 = l4 ** 3 / (3 * 2 ** 0.5)
v5 = l5 ** 3 / 12 * (5 * (3 + 5 ** 0.5) / 2) ** 0.5
print(v3 + v4 + v5)

import math

a,b,c=map(float,input().split())
ans=0.0
ans += float(math.pow(a,3)*math.sqrt(2)/12);
ans += float(math.pow(b,3)*math.sqrt(2)/6);
ans += float(5*math.pow(c,3)*math.tan(math.radians(54))*math.sqrt(1-1/(4*math.cos(math.radians(54))*math.cos(math.radians(54))))/12);
print("%.20f" % ans)

a, b, c = map(int, input().split())

v = a**3/6/2**.5
v += b**3/3/2**.5
v += c**3*(5 + 5**.5)/24

print(v)

import math
a,b,c = list(map(int,input().split()))
v1 = (math.sqrt(2)*a**3)/12
v2 = b**3/(3*math.sqrt(2))
x = c/(2*math.cos(0.9424777960769379717))
v3 = (5*c**2*math.tan(0.9424777960769379717)*math.sqrt(c**2-x**2))/12
print(v1+v2+v3)


import math
l1, l2, l3 = list(map(int, input().split()))
m1 = l1 * l1 - l1 * l1 / 4
h1 = math.sqrt(m1 - m1 / 9)
v1 = l1 * math.sqrt(m1) * h1 / 6

m2 = l2 * l2 - l2 * l2 / 4
h2 = math.sqrt(m2 - l2 * l2 / 4)
v2 = l2 * l2 * h2 / 3

m3 = l3 * l3 - l3 * l3 / 4
x = l3 * math.tan(54 * math.pi / 180) / 2
h3 = math.sqrt(m3 - x * x)
s3 = 5 * l3 * l3 / math.tan(math.pi / 5) / 4
v3 = s3 * h3 / 3

print(v1 + v2 + v3)


import math

l3, l4, l5 = list(map(int, input().split(' ')))
v3 = l3 ** 3 * math.sqrt(2) / 12
v4 = l4 ** 3 / math.sqrt(2) / 3
alpha = math.pi / 5
v5 = 5 / 12 * l5 ** 3 / math.tan(alpha) * math.sqrt(1 - 1 / (4 * math.sin(alpha) ** 2))
print("%.11f" % (v3 + v4 + v5))

def cat(h, c):
    return (h * h - c * c) ** 0.5

l3, l4, l5 = list(map(float, input().split()))

s3 = l3 * l3 * 3. ** 0.5 / 4.
s4 = l4 * l4
s5 = (l5 * l5 * (25. + 10 * (5 ** 0.5)) ** 0.5) / 4.

r3 = l3 / (3. ** 0.5)
r4 = l4 / (2. ** 0.5)
r5 = l5 / 10. * (10. ** 0.5 * (5. + 5. ** 0.5) ** 0.5)

h3 = cat(l3, r3)
h4 = cat(l4, r4)
h5 = cat(l5, r5)

v3 = s3 * h3 / 3.
v4 = s4 * h4 / 3.
v5 = s5 * h5 / 3.
print(v3 + v4 + v5)



from math import sqrt as s

x, y, z = map(int, input().split())

print(pow(x, 3) * (1 / 6 / s(2)) + pow(y, 3) * (s(2) / 6) + pow(z, 3) * ((5 + s(5)) / 24))

import math

def DegToRad(x):
	return (math.acos(-1) / 180) * x
	

l3, l4, l5 = map(int, input().split())
v3 = l3 * l3 * l3 * math.sqrt(2) / 12
v4 = l4 * l4 * l4 * math.sqrt(2) / 6
a = l5; b = a / math.sqrt(2 - 2 * math.cos(DegToRad(72))); h = math.sqrt(a * a - b * b); s = b * b * math.sin(DegToRad(72)) * 2.5; v5 = s * h / 3;
print(v3 + v4 + v5)

import math

l3, l4, l5 = list(map(int, input().split(' ')))

print(math.sqrt(2)*l3*l3*l3/12 + math.sqrt(2)*l4*l4*l4/6 + (5+math.sqrt(5))*l5*l5*l5/24)


a,a1,a2 = map(int,input().split())
print(a**3 / 6 / 2**.5 + a1**3 * 2**.5 / 6 + a2**3 * (5 + 5 ** .5) / 24)

sq2 = 2**0.5
def PyraVolume(number, edge_length):
    el3 = edge_length**3
    if number == 3:
        return el3 / (6 * sq2)
    elif number == 4:
        return el3 / (3 * sq2)
    elif number == 5:
        return el3 * (5 + 5**0.5) / 24

a, b, c = list(map(int, input().split()))
print(PyraVolume(3, a) + PyraVolume(4, b) + PyraVolume(5, c))


3
# Copyright (C) 2016 Sayutin Dmitry.
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; version 3
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; If not, see <http://www.gnu.org/licenses/>.

import math

a, b, c = list(map(int, input().split()))
v1 = (a ** 3) * (2 ** 0.5) / 12
v2 = (b ** 3) * (2 ** 0.5) / 6

phi = 2 * math.pi / 5
L = c / ((2 - 2 * math.cos(phi)) ** 0.5)
v3 = 2.5 * L * L * math.sin(phi) * ((c * c - L * L) ** 0.5) / 3

print(v1 + v2 + v3)


import math
ns = [3,4,5]
L = list(map(int, input().split()))
PI = math.acos(-1)
ans = 0
for n, l in zip(ns, L):
    ang = PI / n
#    l / 2 / r = math.cos(ang)
    r = l / 2 / math.sin(ang)
    S = n * math.sin(2*ang) * r * r / 2
    h = (l**2 - r**2)**0.5
#   print(S,h)
    ans += S * h / 3;
print("%.10f" % (ans))