# -*- coding: utf-8 -*-

def gcd(a):
    for i, n in enumerate(a): a[i] = abs(n)
    a.sort()
    min = a[0]
    result = 1
    for i in range(2, min+1):
        flag = True
        for j in a:
            if j % i != 0: flag = False
        if flag == True: result = i
    return result

def readeqn(eqn,list):
    for i in list:
        eqn[i] = input(i[0]+'=')
    if eqn['A'] == 0 and eqn['B'] == 0:
        raise TypeError("No Both Zero!")

def simeqn(eqn,list):
    eqn_gcd = gcd(eqn.values())
    print eqn_gcd
    for i in list:
        eqn[i] = eqn[i]/abs(eqn_gcd)

def printeqn(eqn,list):
    eqn_text = ''
    for i in list:
        if eqn[i]>0 and i!='A': eqn_text+= '+'
        eqn_text += str(eqn[i])+list[i]
    print eqn_text+'=0'

def calceqn(eqn,list):
    readeqn(eqn,list)
    simeqn(eqn,list)
    printeqn(eqn,list)

# -- Read eqn1 --
print 'Type Ax²+By²+C=0'
list = ['A','B','C']
list1 = {'A':'x', 'B':'y', 'C':''}
eqn1 = {'A': 0, 'B': 0, 'C': 0}

calceqn(eqn1,list1)

# -- READ eqn2 --
print 'Type Ax²+By²+Dx+Ey+F=0'
list = ['A','B','D','E','F']
list2 = {'A':'x²', 'B':'y²', 'D':'x', 'E':'y', 'F':''}
eqn2 = {'A':0, 'B':0, 'D':0, 'E':0, 'F':0}

calceqn(eqn2,list2)