#!/usr/bin/env python3

def shift(
        number, 
        shifts, 
        initialSubtraction, 
        currentShiftIteration, 
        currentSubtractionIteration, 
        permutations):

    for b in range(shifts):
        if currentShiftIteration >= 4:
            return
        number = number << 1
        currentShiftIteration += 1
        permutations.append(number)
        initialSubtraction = (initialSubtraction << 1) + 1
        subtract(number, shifts, initialSubtraction, currentShiftIteration, currentSubtractionIteration, permutations)

    return

def subtract(
        number, 
        subtractions, 
        initialSubtraction, 
        currentShiftIteration, 
        currentSubtractionIteration, 
        permutations):

    subtractionValue = initialSubtraction

    for b in range(subtractions):
        if currentSubtractionIteration >= 4:
            return
        number -= subtractionValue
        currentSubtractionIteration += 1
        subtractionValue = subtractionValue << 1
        permutations.append(number)
        shift(number, (subtractions - 1), subtractionValue, currentShiftIteration, currentSubtractionIteration, permutations)

def run_algorithm():
    permutations = [31]
    shift(permutations[0], 4, 0, 0, 0, permutations)
    # permutations.sort(key=int)
    print(permutations)
    print(len(permutations))

if __name__ == '__main__':
    run_algorithm()