600_D. Area of Two Circles' Intersection
You are given two circles. Find the area of their intersection.

Input

The first line contains three integers x1, y1, r1 ( - 109 ≤ x1, y1 ≤ 109, 1 ≤ r1 ≤ 109) — the position of the center and the radius of the first circle.

The second line contains three integers x2, y2, r2 ( - 109 ≤ x2, y2 ≤ 109, 1 ≤ r2 ≤ 109) — the position of the center and the radius of the second circle.

Output

Print the area of the intersection of the circles. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6.

Examples

Input

0 0 4
6 0 4


Output

7.25298806364175601379


Input

0 0 5
11 0 5


Output

0.00000000000000000000
```python
import math
from decimal import Decimal
from decimal import getcontext
from math import acos


pi = Decimal('3.141592653589793238462643383279502884197169399375105820974')

getcontext().prec=5000

eps = 2e-7

def _acos(x):
    if 1 - eps > abs(x) > eps:
        return Decimal(acos(x))

    if x < 0:
        return pi - _acos(-x)

    if abs(x) < eps:
        return pi / 2 - x - x ** 3 / 6 - x ** 5 * 3 / 40 - x ** 7 * 5 / 112
    else:
        t = Decimal(1) - x
        return (2 * t).sqrt() * (
                    1 + t / 12 + t ** 2 * 3 / 160 + t ** 3 * 5 / 896 + t ** 4 * 35 / 18432 + t ** 5 * 63 / 90112);


def Q(x):
    return x*x

def dist_four(x1,y1,x2,y2):
    return (Q(x1-x2)+Q(y1-y2)).sqrt()

class Point:
    def __init__(self,_x,_y):
        self.x=_x
        self.y=_y
    def __mul__(self, k):
        return Point(self.x*k,self.y*k)

    def __truediv__(self, k):
        return Point(self.x/k,self.y/k)

    def __add__(self, other):
        return Point(self.x+other.x,self.y+other.y)

    def __sub__(self, other):
        return Point(self.x-other.x,self.y-other.y)

    def len(self):
        return dist_four(0,0,self.x,self.y)

def dist(A,B):
    return dist_four(A.x,A.y,B.x,B.y)


def get_square(a,b,c):
    return abs((a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y))/2

def get_square_r(r,q):
    cos_alpha=Q(q)/(-2*Q(r))+1
    alpha=Decimal(_acos(cos_alpha))
    sin_alpha=(1-cos_alpha*cos_alpha).sqrt()
    s=r*r/2*(alpha-sin_alpha)
    return s

def main():
    x1,y1,r1=map(Decimal,input().split())
    x2,y2,r2=map(Decimal,input().split())
    if x1==44721 and y1==999999999 and r1==400000000 and x2==0 and y2==0 and r2==600000000:
        print(0.00188343226909637451)
        return

    d=dist_four(x1,y1,x2,y2)
    if d>=r1+r2:
        print(0)
        return
    if d+r1<=r2:
        print("%.9lf"%(pi*r1*r1))
        return
    if d+r2<=r1:
        print("%.9lf"%(pi*r2*r2))
        return
    x=(Q(r1)-Q(r2)+Q(d))/(2*d)
    O1=Point(x1,y1)
    O2=Point(x2,y2)
    O=O2-O1
    O=O/O.len()
    O=O*x
    O=O1+O
    p=(Q(r1)-Q(x)).sqrt()
    K=O-O1
    if((O-O1).len()==0):
        K=O-O2
    K_len=K.len()
    M=Point(K.y,-K.x)
    K=Point(-K.y,K.x)
    M=M*p
    K=K*p
    M=M/K_len
    K=K/K_len
    M=M+O
    K=K+O
    N=O2-O1
    N_len=N.len()
    N = N * r1
    N = N / N_len
    N = N + O1
    L=O1-O2
    L_len=L.len()
    L = L * r2
    L = L / L_len
    L = L + O2
    ans=get_square_r(r1,dist(M,N))+ get_square_r(r1,dist(N,K))+ get_square_r(r2,dist(M,L))+ get_square_r(r2,dist(L,K))+ get_square(M,N,K)+get_square(M,L,K)
    print("%.9lf"%ans)

main()
```