# Time:  O(n^2)
# Space: O(n)

class Solution(object):
    def largestDivisibleSubset(self, nums):
        """
        :type nums: List[int]
        :rtype: List[int]
        """
        if not nums:
            return []

        nums.sort()
        dp = [1] * len(nums)
        prev = [-1] * len(nums)
        largest_idx = 0
        for i in xrange(len(nums)):
            for j in xrange(i):
                if nums[i] % nums[j] == 0:
                    if dp[i] < dp[j] + 1:
                        dp[i] = dp[j] + 1
                        prev[i] = j
            if dp[largest_idx] < dp[i]:
                largest_idx = i

        result = []
        i = largest_idx
        while i != -1:
            result.append(nums[i])
            i = prev[i]
        return result[::-1]