from mpmath import *

u=mpi(0)

def h(x):
    return iv.exp(u*(x-1))

def f_1(x,a):
    return h(x)*iv.exp(a*(x-1))

def h_1(x,y,a):
    return (1-y*(u+a))*f_1(x,a)

def L_3(f):
    def g(x):
        return (x+3)/4 * f((x+2)/3)**3 + (x+2)/2 * ( f((x+1)/3)**2 - f((x+2)/3)*f((x+1)/3)**2 ) - (x+1)/4 * (f((x+2)/3)**2 * f(x/3) + 2*f((x+1)/3)*f(x/3) - 2*f((x+2)/3)*f((x+1)/3)*f(x/3) - f(x/3))
    return g

def H_3(f):
    def g(x):
        return (x+3)/4 * f((x+2)/3)**3 + (x+2)/3 * ( f((x+1)/3)**2 - f((x+2)/3)*f((x+1)/3)**2 ) - (x+1)/12 * (f((x+2)/3)**2 * f(x/3) + 2*f((x+1)/3)*f(x/3) - 2*f((x+2)/3)*f((x+1)/3)*f(x/3) - f(x/3))
    return g

def G_1(f):
    def G_1f(x):
        a=L_3(f)(x/2)
        b=L_3(f)((x+1)/2)
        c=H_3(f)(x/2)
        d=H_3(f)((x+1)/2)

        return (x/3)*a+((x+1)/3)*b**2-(x/3)*a*b+(1/3)*c+(1/3)*b*d-(1/3)*b*c
    return G_1f

m=1

while m < 341:
    f_2=G_1(h)
    for a in map(mpi, [1/16,1/32,3/256]):
        for j in range(256):
            A = f_2( mpi(j/256) )
            B = h_1( mpi(j+1)/256, mpi(1/256), a)
            if A.b>B.a:
                break
        else: break
    else: break

    print(m)
    m=m+1
    u+=a
print(m, u)