#!/usr/bin/env python3

#Naive and buggy
#check 2 + 8 + 6 + 12 + 48 = 76 per quad

from fractions import Fraction
from itertools import permutations, combinations, starmap

def new_count(c, x):
    while x[c] == c+1:
        c+=1
    return c-1

def test():
    c = 27
    best = (1,2,3,4)
    best_r = []
    for i in combinations(range(1, 10), 4):
        r = sorted(list(main(i)))
        if r[c] == c+1:
            best_r = r
            best = i
            c = new_count(c, r)
    return best, c
            

def naive(s):
    r = []
    for perm in permutations(s, 4):
        r += alt_prod(perm)
    return r

def alt_prod(s):
    a = add(s[0], mlt(s[1], add(s[2], set([s[3]]) )))
    b = mlt(s[0], add(s[1], mlt(s[2], set([s[3]]) )))
    return [a, b]

def main(s):
    r = []
    prods = tree(s, mlt)
    sums  = tree(s, add)
    r += fold(s[::-1], sums[1], mlt)
    r += fold(s[::-1], prods[1], add)
    r += fold(sums[0][:3], sums[0][3:], mlt_sets)
    r += fold(prods[0][:3], prods[0][3:], add_sets)
    r += fold(sums[0], prods[0][::-1], add_sets)
    r += fold(sums[0], prods[0][::-1], mlt_sets)
    r += [add(s[-1], sums[1][0]), mlt(s[-1], prods[1][0])]
    r += naive(s)
    return set([int(x) for x in set.union(*r) if x == int(x)])

def fold(a, b, f):
    return starmap(f, zip(a, b))

def tree(s, f):
    sc = []
    tr = []
    for i in range(4):
        for j in range(i+1, 4):
            sc.append(f(s[i], set([s[j]]) ))
            for k in range(j+1, 4):
                tr.append(f(s[k], sc[-1]))
    return sc, tr

def add_sets(a, b):
    r = set()
    for i in a:
        r.update(add(i, b))
    return r

def mlt_sets(a, b):
    r = set()
    for i in a:
        for j in b:
            r.add(i*j)
    return r
def add(e, x):
    r = set()
    for i in x:
        r.add(e+i)
        if e != i:
            r.add(abs(e-i))
    return r

def mlt(e, x):
    r = set()
    for i in x:
        r.add(e*i)
        r.add(Fraction(1, e) * i)
        r.add(Fraction(1, i) * e)
    return r

a = set([2, 3, 45, 8])
b = set([4, 6,7])

r = test()
s = ''.join(map(str, r[0]))
print(s)