class Solution:
    def maxHeightOfTriangle(self, red: int, blue: int) -> int:
        # Let's try starting with both colors and take the maximum result
        return max(self.tryHeight(red, blue), self.tryHeight(blue, red))

    def tryHeight(self, color1: int, color2: int) -> int:
        height = 0
        row = 1

        # Keep alternating colors
        while True:
            # Try to use color1 for odd rows
            if row % 2 == 1:
                if color1 >= row:
                    color1 -= row
                    height += 1
                else:
                    break
            # Try to use color2 for even rows
            else:
                if color2 >= row:
                    color2 -= row
                    height += 1
                else:
                    break
            row += 1

        return height