# Pastebin VVrrJwPU
function fact(z)
	z=z+1
    local m=math
	local pi,e=m.pi,m.exp(1)
	local g = 7
	local p = {0.99999999999980993, 676.5203681218851, -1259.1392167224028,
     771.32342877765313, -176.61502916214059, 12.507343278686905,
     -0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7}
    if z < 0.5 then
        return pi / (m.sin(pi*z) * gamma(1-z))
    else
        z = z-1
        x = p[1]
        for i=1,g+1 do
            x = x+p[i+1]/(z+i)
		end
		t = z + g + 0.5
        return m.sqrt(2*pi) * m.pow(t,z+0.5) * m.exp(-t) * x
	end
end