Problem: 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

Solution (in PYTHON3):

Solution:
import decimal
from decimal import Decimal

pi = Decimal('3.14159265358979323846264338327950288419716939937510')
decimal.getcontext().prec = 40


def cos(x):
    """Return the cosine of x as measured in radians.

    The Taylor series approximation works best for a small value of x.
    For larger values, first compute x = x % (2 * pi).

    >>> print(cos(Decimal('0.5')))
    0.8775825618903727161162815826
    >>> print(cos(0.5))
    0.87758256189
    >>> print(cos(0.5+0j))
    (0.87758256189+0j)

    """
    decimal.getcontext().prec += 2
    i, lasts, s, fact, num, sign = 0, 0, 1, 1, 1, 1
    while s != lasts:
        lasts = s
        i += 2
        fact *= i * (i - 1)
        num *= x * x
        sign *= -1
        s += num / fact * sign
    decimal.getcontext().prec -= 2
    return +s


def sin(x):
    """Return the sine of x as measured in radians.

    The Taylor series approximation works best for a small value of x.
    For larger values, first compute x = x % (2 * pi).

    >>> print(sin(Decimal('0.5')))
    0.4794255386042030002732879352
    >>> print(sin(0.5))
    0.479425538604
    >>> print(sin(0.5+0j))
    (0.479425538604+0j)

    """
    decimal.getcontext().prec += 2
    i, lasts, s, fact, num, sign = 1, 0, x, 1, x, 1
    while s != lasts:
        lasts = s
        i += 2
        fact *= i * (i - 1)
        num *= x * x
        sign *= -1
        s += num / fact * sign
    decimal.getcontext().prec -= 2
    return +s


def acos(x):
    # binary search
    def f(xx):
        return cos(xx) - x

    a = 0
    b = pi
    xx = (a + b) / 2
    fxx = f(xx)
    while abs(fxx) > Decimal('0.0000000000000000000001'):
        if fxx > 0:
            a = xx
        else:
            b = xx
        xx = (a + b) / 2
        fxx = f(xx)
        # print (xx, fxx)
    # print (f"diff {xx-rel(x)}")
    return xx


def part(ra, rb, d2):
    d = Decimal(d2).sqrt()
    x = (ra ** 2 - rb ** 2 + d2) / (2 * d)
    a = Decimal(acos(x / ra))
    b = Decimal(acos((d - x) / rb))
    part_a = ra ** 2 * a - ra * ra * sin(a) * cos(a)
    part_b = rb ** 2 * b - rb * rb * sin(b) * cos(b)
    return part_a + part_b

x1, y1, r1 = map(int, input().split())
x2, y2, r2 = map(int, input().split())
dist2 = (x1 - x2) ** 2 + (y1 - y2) ** 2



if dist2 > (r1 + r2) ** 2:
    print(0)
elif dist2 <= (r1 - r2) ** 2:
    print(pi * min(r1, r2) ** 2)
else:
    print(part(r1, r2, dist2))