import time
class Solution(object):
    def largestDivisibleSubset(self, nums):
        f = {-1: set()}
        for item in sorted(nums):
            f[item] = max((f[d] for d in f if not item % d), key=len) | {item}
        return list(max(f.values(), key=len)) 
        
        """
        for i in xrange(1, len(nums)):
            f.append([nums[i]])
            f[i] = max([f[j] for j in range(1, len(f)) if nums[i] % f[j-1][-1] == 0], key=len) + [nums[i]]
        return list(max(f, key=len))
        """
sol = Solution()
nums = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99]
#print nums
start = time.time()
print sol.largestDivisibleSubset(nums)
print time.time() - start
