# https://leetcode.com/problems/construct-the-rectangle/
# A web developer needs to know how to design a web page's size. So, given a specific rectangular web page’s area, your job by now is to design a rectangular web page, whose length L and width W satisfy the following requirements:
#
# The area of the rectangular web page you designed must equal to the given target area.
# The width W should not be larger than the length L, which means L >= W.
# The difference between length L and width W should be as small as possible.
# Return an array [L, W] where L and W are the length and width of the web page you designed in sequence.
#
# Example 1:
#
# Input: area = 4
# Output: [2,2]
# Explanation: The target area is 4, and all the possible ways to construct it are [1,4], [2,2], [4,1].
# But according to requirement 2, [1,4] is illegal; according to requirement 3,  [4,1] is not optimal compared to [2,2]. So the length L is 2, and the width W is 2.
# Example 2:
#
# Input: area = 37
# Output: [37,1]
# Example 3:
#
# Input: area = 122122
# Output: [427,286]


class Solution:
    def constructRectangle(self, area: int) -> List[int]:
        import math
        maxv = 0
        for i in range(2, int(math.sqrt(area)) + 1):
            if area % i == 0:
                maxv = i if i > maxv else maxv
        if maxv > 0:
            return area // maxv, maxv
        return area, 1
