from itertools import permutations

SIZE = 4

def enforceIndexes(cindex):
    # for example,
    # clue #1 enforces cells 1,5,9,13 (of index),
    # clue #6 enforces cells 11,10,9,8. (watch out for the sequence)
    if 0 <= cindex < SIZE: return [cindex + SIZE * x for x in range(SIZE)]
    if SIZE <= cindex < SIZE * 2: return [(cindex - 4) * SIZE + SIZE - 1 - x for x in range(SIZE)]
    if SIZE * 2 <= cindex < SIZE * 3: return [3 * SIZE - 1 - cindex + 4 * (SIZE - 1 - x) for x in range(SIZE)]
    if SIZE * 3 <= cindex < SIZE * 4: return [(4 * SIZE - 1 - cindex) * 4 + x for x in range(SIZE)]
    else: raise ValueError('Wrong cindex!')

def possibleCombs():
    cluePossibles = [[] for i in range(SIZE)]
    for i in permutations([x+1 for x in range(SIZE)]):
        clue = 0
        highest = 0
        for v in i:
            if v > highest:
                clue += 1
                highest = v
        cluePossibles[clue - 1].append(i)
    return cluePossibles

def buildbinary(clues):
    # binary map:
    # 01101 - possible for 1,2,4
    # 01000 - possible for 4
    # 11101 - fixed for 2
    binary = [2 ** SIZE - 1 for i in range(SIZE ** 2)]
    cluePossibles = possibleCombs()
    cluePossibleLens = list(map(len, cluePossibles))
    # fill row/columns with clues that restricts cells the most first (i.e. clue = 4)
    fillSequence = sorted([i for i in range(SIZE ** 2) if clues[i] > 0], key = lambda x: cluePossibleLens[clues[x] - 1])
    clueTrack, clueSearchIndex, layerIndex = [], [], 0
    for i in fillSequence:
        clueTrack.append((i, cluePossibles[clues[i] - 1]))
        clueSearchIndex.append(0)
    while clueSearchIndex[0] < len(clueTrack[0][1]):
        # so not all clues have been proved invalid

def binaryFillLine(binary, clueIndex, line)





def solve_puzzle(clues):

    return