def iteration_lagrange(x0, q0, m, epsilon, f):
    def maj_test(xn,xnm1):
        return f(xn)!=0 and abs(xn-xnm1)>epsilon

    n=0
    test=f(x0)!=0
    X=[x0]
    xnm1=x0
    xn=float(x0-f(x0))/q0
    qn=q0
    print(xn,q0)
    while n<=m and test:
        qn=float((f(xn)-f(xnm1)))/(xn-xnm1)
        xnm1=xn
        xn=xnm1-f(xnm1)/qn

        X+=[xn]
        test=maj_test(xn,xnm1)
        n+=1
    return (n,X)

////////////////////////////////////////////////////////////////////////////
print(iteration_lagrange(pi/4,1,200,0.0000001,f))