# Time:  O(n * sqrt(n))
# Space: O(n)

class Solution(object):
    _num = [0]
    def numSquares(self, n):
        """
        :type n: int
        :rtype: int
        """
        num = self._num
        while len(num) <= n:
            num += min(num[-i*i] for i in xrange(1, int(len(num)**0.5+1))) + 1,
        return num[n]